When Marty is driving the taxi at night in the early part of the film a car can clearly be seen in front of his. This is supposed to be set in 1988 yet the car in front is a Ford which dates 2006 at least.
In an early scene in the film, Martin looks over at Ray who is standing amongst a group of children. Some of the children, obviously extras from the area, are wearing anachronistic clothing such as polyester track pants.
When Marty walks into the bakery to see his girlfriend and child, a 'Scores on the Doors' sign is visible on the door as he opens it - 'Scores on the Doors' didn't come into effect until 2005 while the events in the film are set in and around 1990.
In the scene where he is tasked to deliver the message he gets ino his Rover SD1 car. As his handler exits the car he bangs the steering wheel centre boss in anger and the car horn is sounded. This is an error as the horn switch on this vehicle was on the end of a stalk, not the steering wheel.