Zefram Cochrane puts his hand on the body of the telescope when Geordi invites him to look at the Enterprise. No one who knew anything about astronomy would ever do this as it would change the alignment of the telescope.
After the destruction of the Borg sphere, Picard asks where the Borg were firing on, and Riker heads towards the Science station on his right to read the coordinates from the display. Just a moment after, he asks Lt. Hawk (who is at the helm) for the damage done on the surface. Hawk states that "long-range sensors are still off-line", but at that distance away from Earth, short-range sensors would have sufficed. Furthermore, Hawk shouldn't even be capable of reading long-range science sensors from the helm console, and even if he could, Riker is still next to the science station, with the science officer next to him, AND the information about the surface is still on the display, so there is no need to ask the helmsman for it.
Picard misquotes Moby Dick when he says, "And he piled upon the whale's white hump the sum of all the rage and hate felt by his whole race. If his chest had been a cannon, he would have shot his heart upon it." The actual quote by Herman Melville reads, "He piled upon the whale's white hump the sum of all the general rage and hate felt by his whole race from Adam down; and then, as if his chest had been a mortar, he burst his hot heart's shell upon it."
When Picard walks around the ship with Lily and she asks how big the ship is, Picard says it has 24 decks. But about 6 minutes earlier in the movie, Lieutenant Daniels tells Worf that the Borg have control over "decks 26 up to 11". The film's text commentary suggests several possible explanations for this inconsistency, including the idea that decks 25 and 26 were top secret, so Picard had to mislead Lily in case the Borg assimilates her. It's also possible that decks aren't numbered in a sequence, so that a ship with 24 decks can actually have deck 26. However, no convincing explanation exists.
When Picard refuses to order self-destruct, insults Worf and then storms off the bridge, Dr. Crusher simply accepts his irrational behavior and tells Lilly the discussion is over. This is seriously incongruous with her well-established character. She would have pursued Picard and berated him as Lily did.
During Picard's briefing of the commando teams about their objectives, they arm themselves with phaser rifles. As Picard and Data approach the Borg lair, their team is holding a different kind of weapon. During the subsequent fight with the Borg, everyone is again holding the first type of phaser.
When the camera gets a shot of the holodeck doors right before Picard shoots the Borg wall with his phaser, the ID sticker on the door reads "08 HOLOSUITE 4". When the Borg force their fingers through the seam to open the door, the ID sticker now says "0820 HOLODECK 07".
On the Defiant when Worf yells "Report!" he's on the ground just holding the Captain's chair arm, then the camera changes and he's suddenly in the chair. Next, when Worf is saying "..day to die!" some one is behind Worf moving toward the bridge door to leave, but disappears when the camera switches to the angle with the helmsman, but the person appears again when Worf says "Prepare for ramming speed!" and finally leaves the bridge.
When we first see the Defiant making its attack run at the Borg Cube it is firing pulse phasers. Once the Borg Cube is in full view you can see the explosive damage the Defiant's hits are causing, however, in the seconds before the Cube is in full view you can still see the Defiant's shots hitting the cube with no explosive damage, almost like they forgot to add in the explosions.
When Lily passes out from the radiation, her gun should have made a sound as it fell to the ground (which does happen briefly, before Data catches her). However, no such sound is heard, and the firearm is outright missing in the subsequent shots.
When Barclay is swooning at having met Cochrane, an Enterprise crew member can be seen walking behind him and Geordi. One scene doesn't show the man carrying a suitcase then after Geordi chastises reg the man suddenly appears and begins to walk as if he had been waiting for his cue to continue.
When Picard goes into the conference room to work on new modulations he and Lily enter it from the left side of the Bridge. When they go back onto the Bridge after Lily convinces him to blow up the ship, they walk through the same door in the conference room, yet come out on the right side.
When Picard tries to convince Lily that he is a friend and asks for the phaser, she is seen starting to lower it and hand it over to him. The next time the camera is on her, she is clearly pointing the phaser at him. Only abit later does she lower it and hand it to Picard.
Early in the film, when Deanna finds Dr. Cochrane, it is still night. Immediately after she passes out, the very next shot is one from space of North America in daylight. (While it is arguably the case that the stories on land and on the Enterprise diverge from temporal sequence, it is too early in the film at that point for them to have done so.)
When the Borg initially invade the enterprise Picard & Worf form separate search groups both search groups eventually arrive at the same place engineering 16 all corridors leading to this door are surrounded by Borg technology. Towards the end of the movie Picard attempts to rescue Data from the Borg Picard arrives at exactly the same door Engineering 16 however all forms of Borg Technology have disappeared.
When Picard is escorting Lily through the ship 49 minutes into the movie, they step through a doorway and a member of the film crew is visible in the corridor behind them, wearing a blue and white striped shirt with a radio clipped to his belt.
The Enterprise is sent to patrol the edge of the neutral zone between the Federation and the Romulan Empire when the Battle of Sector 001 occurs. When Picard orders the Enterprise to return to Earth to engage the Borg, the ship seemingly gets back to Earth in a short time. However, since Star Trek maps list the Neutral Zone as being about 30 light years from Earth, it would take the Enterprise over 7 days to return to Earth at Warp 9.
When the Phoenix launches we see Cochrane, Riker and LaForge rocking back and forth in their seats. The thrust of launch is constant, and substantial, so they would not rock but rather be forced firmly and steadily back into their seats until the thrust ended. Also, their seats offer totally inadequate head support so it's quite likely all would have died from broken necks shortly after launch.
Early in the movie after Picard has decided to disregard orders and is returning to Earth we see him in his quarters looking out into space with several stars twinkling. They shouldn't be twinkling as there is no atmosphere for the light to travel through which is what causes stars to twinkle.
Supposedly, Cochrane used an ICBM as the launch vehicle for the Phoenix, launching from the missile silo. But controls for the silo are nowhere near the silo itself because the exhaust would incinerate the crew monitoring the launch.
Holodeck re-creations of Earths early time periods are famous for their highly accurate representations. In the movies holodeck scene, at least one African-American couple is seen on the dance floor. This representation can be questioned, considering that the detective novel is placed around 1940s America. In which case the night clubs were all highly segregated at that time. Although, it can be argued that the computer compensates for the evolved culture of 400 years in the future, however that also means that the computer adds representations that are not chronologically accurate.
When Lily is shooting at Data in the missile silo, after she runs out of ammunition her gun makes several metallic clicks. This is apparently meant to indicate the weapon is empty. In reality the gun's bolt would lock open after the last round was fired. Even if she continued to pull the trigger, it would not make any such sound.
When Geordi is asking Cochrane to look at the intermix chamber blueprints, he is wearing sunglasses, even though his artificial eyes don't require protection from the sun. The sunglasses are probably needed in case a local comes looking around. Only Cochrane and Lily knew about time travelers, and Geordi's futuristic implants could blow their cover. Geordi used dark glasses for the same purpose in Star Trek: The Next Generation: Time's Arrow: Part II as well.
Cmdr Riker unplugs the jukebox when he first meets Dr Cochrane. A few minutes later Dr Cochrane appears to simply hit the jukebox to turn it back on. However, in the background during the last few lines of Riker and Troi's conversation, you can see Cochrane bend down beside the jukebox, (presumably) to plug it in. He then hits it to restart it.
How did Picard know about the weak point in the Borg cube? He had been assimilated in "Star Trek: The Next Generation; The Best OF Both Worlds". After being rescued and disconnected from the Borg Collective, he stated that he remembered everything. Since all Borg share knowledge through the Collective, Picard learned about the design and construction of a Borg cube. Thus he knew its weak point. Also, just before he gave Data the coordinates, he heard a Borg chatter in his head (the Queen later confirmed that he wasn't imagining it), so it's possible that he intercepted a report about some kind of damage or dangerous power buildup in that section, which just turned it into the cube's Achilles heel.
When the away team beams down to the surface for the first time, a visible breath due to cold weather can be seen coming from Data. While it may seem strange that an android has to breathe, it's not an error - Data does have a functional respiratory system. This issue was addressed in Star Trek: The Next Generation: Birthright, Part I.
At first glance, there is no reason for the Borg to travel to Earth in the 24th century. If their plan was to invade Earth in 21st century, the Borg could have done their time-travel from a safe faraway place, then travel to Earth, or just send the Earth's coordinates to the 21st century Borg so the latter invade the Earth instead. However, even though there was no Federation in the 21st century, its future territory was occupied by several advanced space-bearing species, often at war with each other (Vulcans and Klingons in particular). Apparently the Borg figured that a small sphere has less chances of reaching Earth in the 21st century than a fully armed cube in the 24th. The point is that they made the right choice - the idea with the cube worked just fine and Starfleet failed to stop the sphere. It is also possible that after incorporating the time machine and weapons, there was no place left in the sphere for warp engines or long range communicator. In any case, we don't really know Borg's actual plan. The Queen said that they had many goals. Perhaps pulling the Enterprise into the past for safe assimilation was one of them.
In the holodeck scene, it is established that the Borg shields cannot fend off crude solid projectiles. In the deflector scene, Worf kills one with a Klingon blade weapon called a "mak'leth". Why didn't Picard simply order the crew to replicate obsolete firearms and swords to fight with? Because Borg can adapt to (almost) anything after a short while. Using old weapons would have been no more effective than reconfiguring phasers. But why did these weapons work in the first place, if Borg can adapt to them and probably encountered such weapons before? Because Borg don't use every adaptation from every weapon they have ever encountered - that would be highly impractical and inefficient. Instead, they simply re-adapt for any given mission.
While Picard, Worf and Hawke are trying to disable the "interplexing beacon" the Borg are building on top of the deflector dish, smoke or steam can be seen rising up in such a way it only can in an atmosphere. Steam/smoke would normally dissipate in a vacuum, zero gravity, in all directions, if it's not propelled, and if it is propelled "upward", then it will continue to "rise" and won't come back "down" as seen in the movie. However, all this is true if the electric charge is taken out of the equation. The steam is likely ionized (positively charged), if not for functional purposes (we know that plasma is often used in the deflector), then because of Picard's phaser fire. Picard also mentions that the dish is charged with anti-protons (negative charge), which perfectly explains why the positively charged steam is pulled back toward the dish. Plasma behavior in an unknown electromagnetic field can be complicated enough to explain all the apparent inconsistencies of its motion in space.
At one scene, Zefram Cochrane looks at the Enterprise through the telescope from Montana. Two minutes of movie time later, Picard shows the Earth to Lily Sloane, and the ship is over Australia on course to North America (Picard remarks that Montana is coming up soon). However, between those two scenes various incidents of crew fighting the Borg are shown, indicating that some time has passed by. A ship at the presented orbit can go from Montana to Australia in less than a couple of hours. Moreover, the stories on the ship and on the ground aren't connected at that point, so theoretically the second scene could have happened before the first. In any case, there is no obvious error in the ship not being over Montana in the second scene.
If the only people intended to fly the Phoenix were Cochrane and Lily, it would have been built for two, not three as when Riker and LaForge accompany him. However, no one has ever said that Cochrane and Lily were supposed to fly alone. Evidently, there was a third crew member who might have been killed in the Borg attack or became unavailable for some other reason.
When Worf is fighting the Borg from his disabled ship (preparing for ramming speed) he has a huge gash type of wound on his left cheek but when he is brought to the bridge of the Enterprise-E it is completely healed. However, he is brought onto the bridge by Dr. Beverly Crusher, it's more than likely this was a clue that before requesting to be taken to the bridge, the doctor healed Worf's injury- a simple feat with 24th century medical technology as shown in numerous Star Trek works.
Before Picard is beaming down to Earth, he says "Number One, you have the bridge", but when Picard is going back to the Enterprise, Riker is standing behind him. However, this happens later, after the away team secures the Phoenix and much of the crew beams down and starts fixing the ship and looking for Cochrane. In fact, Picard specifically states (just before Crusher and Lily beam out), "Have Riker beam down with a search party."
In the deflector dish scene, Picard is seen shooting a section of the dish to blast one of the Borg with a jet of gas to send that Borg off the ship into space. Later, he's seen making a wild, non-magnetized jump across the dish to the other side without any form of control except for the magnetic boots, across the same jet that blasted the Borg off, without flying into space. It makes sense that the jet is much weaker now because the gas supply is running out. Also, Picard is further away from the jet's origin, which reduces its effect even further. Still, it actually does throw him off course and he ends up being too high, but fortunately, he is able to grab onto a raised part of the hull and climb back down.
When Worf confronts Picard on the bridge and declares that if "he [Picard] was any other man, he would kill him," Worf does not have his sash on. In the bridge scene where Picard decides to destroy the Enterprise Worf has his sash on. Possibly, when Worf was ordered off the bridge he went got it and put it on before returning.
When Picard fires at the wire holding the reflector dish they just detached via MagLock, they zoom out and show a wider angle of them on the outside of the ship.
There is a Borg next to a crewman(possibly Worf). There shouldn't have been a Borg there.
The Borg standing next to Worf is the one he had killed with his mek'leth earlier in the scene.
In the original "Star Trek" Kirk said Cochrane was from Alpha Centauri, not Earth. According to the modern canon, Cochrane was born on Earth and later moved to the Alpha Centauri colony, when it was established thanks to his warp engine, thus solving this inconsistency.
When Picard, Worf, and Hawke begin walking to the deflector dish to stop the Borg we see their shadows and the Sun reflection in their helmets, indicating that they're standing in direct sunlight, yet we also see a multitude of stars every time the sky is visible, which shouldn't be possible even outside of the atmosphere. However, this is a common misconception, based on the fact that photographs of the Moon's surface taken by the Apollo astronauts show starless black skies. But this is just a technical issue. As long as the camera isn't pointed directly at the Sun or any too brightly lit area, and the exposure, sensitivity and "dynamic range" of the camera are large enough, the stars will appear. Indeed, the Apollo astronauts did take a few pictures with plenty of the stars by pointing a camera upward with long exposure, and even managed to see stars with the naked eye by hiding in a shadow of a large boulder.
The Defiant's surviving crew are beamed aboard the Enterprise-E. So why is Worf the only one ever seen? Worf was a high ranking senior officer, who requested the doctor bring him to the bridge. This implies that any other survivors(assuming there were any) were put to work in other sections of the ship- not the bridge- or even held in the sick bay to further treat injuries.
In the deflector scene, right after Picard finished releasing Hawk's control, Hawk steps on the gun to keep Picard from using it, only to Picard's surprise, Hawk has been assimilated. Earlier in the movie on the assault to engineering a security officer opened a hatch only to be assimilated with two needles in his neck. So how is Hawk's suit still pressurized? it's not. Not necessarily. It has been shown that the Borg do not need atmosphere. Hawk's suit could remain breached with no "harm" to the Borg that Hawk has become.
Although it's strongly implied and makes perfect sense that CDs are no longer used by 2063, throughout the warp test flight there is an obvious plastic CD holder hanging on the wall behind Riker. However, it's probably just something that happens to look like a CD holder, or maybe it is an old CD holder that was re-purposed for some other function, which makes sense given the fact that the ship builders are poor scavengers.
The body of the Cochrane's warp-ship is located right between nacelles. It is often assumed, based on other ships designs and outdated trivia from the original series, that there must be a free space between and around the nacelles to generate a warp field, so the Phoenix shouldn't be able to fly at warp. However, that is obviously not true (at least since the original series). There are ships that even keep their warp coils inside the ship's body, including the Defiant (as can be seen in the beginning of the movie), yet they work just fine.
Since the coolant for the Warp Drive could freeze the organic parts of the Borg, they could not have survived without protection in outer space. Actually, Data said that the coolant liquefies organic component, not freezes them. The Borg are impervious to cold.
When outside the Enterprise on the deflector dish, the characters walk on the surface of the ship with magnetic boots as there is no gravity, both characters and weapons float away in different scenes. But when Worf crouches to turn the handle round he appears to place his weapon down on the ship's surface as if there's gravity present. Actually, we never see Worf put down the weapon - it is completely obscured. For all we know it's floating just above the ship's surface throughout the scene. Alternatively, Worf could have found some kind of crevice and jammed the weapon into it so it wouldn't flow away.
The Enterprise traveled back in time to April 4, 2063, "the day before first contact". Later in the movie, Riker states that the flight has to be made before 11:15 AM (on April 5th). Yet when Captain Picard orders engineering teams to begin repairing the Phoenix, he seemingly says, "we have less than forty eight hours before this ship has to be launched", which sounds wrong (even if technically correct) if they have less than 24 hours left. But actually, Picard says "fourteen hours", though he doesn't say it clearly enough, so it does sound a bit like "forty eight hours". Interestingly, even if he had said "forty eight", it wouldn't necessarily have been wrong as well - it's possible that they arrived shortly after midnight on April 4th (Montana time), in which case they had 35 hours until first contact. It's even possible that they arrived at the early evening of April 3rd (Montana time), but Data was using Greenwich time (which makes sense), where it was already after midnight on April 4th, in which case they had over 40 hours. Either way, there is no error here.
When Dr. Crusher is treating Lily in sick bay, she realizes the ship has been infiltrated by the Borg when one of them tries to punch through the sickbay door. However, up to that moment the sickbay staff had no idea the ship had been boarded. So there would be no reason for the automatic door to be locked.
After Picard has convinced Lily he is a friendly, she puts her earlier-acquired phaser in his hand. Shortly before it touches Picard's hand, the emitter lights up, indicating that Alfre Woodard (Lily) has touched the fire button of the prop, which lit up to show the post-production people where to insert a phaser beam effect.
During the battle with the Borg Cube, the Earth is shown in a last quarter phase (right half of it is dark). However, the night side is supposed to be pitch black with city lights, not the slightly darkened version of the day side with no city lights. Also, the cloud patterns across the Pacific ocean change drastically during the relatively short battle.
During the deflector dish sequence set on the outside of the ship, both the sparks that come from a shot Borg and the dust that comes from releasing the Borg transmitter clamps fall to the deflector dish "floor".
When the spaceship 'Phoenix' takes off the people are shown looking at the take-off. At this distance, the people would be all vaporised by the rocket exhaust, or at least be killed by the hot and toxic gases produced by the missile.
When the Phoenix goes into warp, stars appear to be streaking past the ship. The interstellar distances are so huge that even at high warp (let alone Phoenix's low warp) the relative motion of stars would be imperceptibly small to the human eye. Of course, this "error" appears in almost every Star Trek television show or movie. An acceptable explanation is that all this streaking is just some weird optical effect created by the warp field. Since the whole concept of warp drive is well outside of the real physics, it would be pointless to speculate about the nature of this effect. As for the apparent shifting of the stars at sub-light speeds, it's perfectly explainable by the change in ship's trajectory.
When the Phoenix drops out of warp and turns around, we see the Earth and the Moon as they would appear from a distance of just a few million kilometers away (based on a fact that even the Moon's disk is still discernible). It is claimed that a ship in warp should have traversed a much greater distance. However, that's not necessarily true. Although we don't know how fast the Phoenix was going and for how long, it's safe to assume that it didn't go beyond warp 1 (which is equal to the speed of light). Also, the movie shows only 10 seconds of flight (two 5-second cuts), and there is no reason to suggest it took more time than that. This results in a total distance of 3 million kilometers, which is highly consistent with Earth's appearance. Moreover, it was generally assumed that the ship was moving away from Earth the whole time. But when we see Earth through the window, it appears to be growing, indicating that Phoenix is moving toward it. Either the warp flight was on a curved trajectory (we know from the series that it's possible), or that Riker's "throttle back" pushed the ship into reversed course. In both situations, the argument in favor of the goof is weakened even further.
Worf says that "The Moon obscured our warp signature", but a few moments later Lilly looks up and clearly sees the Enterprise as it disappears into the vortex. This is because after the Vulcans landed and stopped scanning the area there was no need to hide anymore and the Enterprise came back to Earth's orbit - it had to do so anyway to beam the crew back up (the Moon is too far away for a transporter beam).
In "ST: TNG, The Best Of Both Worlds Part 2" Picard/Locutus says that Data "will be obsolete in the New Order". Why, then, is the Borg Queen so fascinated with and attracted to Data? At first, she is only interested in Data because he's the only one who can unlock the main computer, but after getting flesh and blood Data becomes a highly advanced cyborg, not a "primitive artificial organism", making him much more interesting. In any case, even Borg are allowed to change their minds.
The Vulcans detect the launch of Zefraim Cochrane's warp vessel but cannot detect the more advanced and uncloaked Enterprise D in orbit. They also cannot detect the warp signatures of the Borg vessel that the Enterprise destroyed or even the wreckage of that vessel in orbit. Actually, Riker explicitly states that in order to be detected by the Vulcans the Phoenix has to break the warp barrier, which, apparently, creates a powerful energy burst that can be detected from afar. Since neither the Enterprise nor the Borg sphere ever went to warp in the 21st century, their warp signature was weak and hard to detect. The Enterprise used the Moon's gravitational field to obscure its signature (as Worf reported) until the Vulcans landed (and stopped scanning the area), and the Borg sphere was destroyed about 24 hours before Vulcans arrived and its remains had crashed to Earth by then (they were later discovered in an episode of the "Enterprise" series).
When the Enterprise reaches the battle and Picard finds out the Admiral's ship has been destroyed, he says to notify the fleet he is taking command of the fleet, even though he doesn't know if he's the ranking officer in the field (in fact, it is later revealed in "Voyager" that admiral Haze did survive this battle). However, Picard didn't assume command because it was proper, but because he was the right man for the job. By this point he was already violating a direct order anyway, so this second act of insubordination would make little difference. The fleet played along because Picard is famous and highly respected, and they probably agreed with Riker that Haze was wrong and Picard should have been in command from the start. Deanna's surprised reaction to Picard assuming control further indicates that Picard was knowingly breaking the rules in this case. Having said that, Picard may have actually had the authority to take command (see Trivia section about Starfleet regulation 191).