Miranda and the other doctors regularly throw around the word "crazy" to refer to patients or Miranda herself, yet this is a stigmatized (and inaccurate) word medical professionals would not use so lightly.
When Miranda flees from solitary after seeing Chloe and crashing into the two guards, she falls backwards with her head towards the solitary. In the next shot, she is lying the other way around, fighting.
When Pete talks to Miranda for the first time after the murder, and is crouched with his back to the cell door, two plastic cups are on the floor. As he rises, the cups have changed positions. One is lying on the floor, facing Pete.
At the end of the movie, they are supposed to be in New York City. However, as Chloe is getting into the cab, you can see a (partially burnt out) Tim Horton's sign in the background. Tim Horton's is a Canadian coffee shop not found in New York. However, in the years after this movie was made, Tim Horton's did open shops in New York.
When Pete is taking Mirandas blood pressure he holds the bell of the stethoscope against her arm with his thumb. This is incorrect for the same reason you don't use your thumb to check someone's pulse. The thumb actually contains a heartbeat too. If you use it to try to listen, as with the stethoscope when taking a blood pressure, or check someones pulse your likely to pick up the sound/beat of your own pulse. If you use your thumb to check your own blood pressure or pulse you will get an incorrect reading, because you'll be hearing/feeling your own heartbeat twice.
When Miranda is telling Doug about the medications that have been used on Chloe, she mispronounces the last drug, Haldol, as "Hadodol." There is no drug called "Hadodol," and the film's closed captioning gives the correct word "Haldol."
When Miranda escaped from her cell the second time, the nurse who tried to close the grated fence door to keep her trapped on the cell floor clearly paused in her efforts to wait for Halle Berry to arrive and push the door back open.
The goof item below may give away important plot points.
After Miranda escapes the institution and travels to the site of Willow Creek, the sheriff refuses to allow her back to the institution because she is now deemed too dangerous, and must stay in the jail. Yet, this development seems backwards. If she is now fine to be kept, without medication, in a jail, it is all the more odd that after the initial murder a judge allowed her to be transferred away from the jail and medicated before the point where she was even awake or cogent.