Continuity mistake: When Buford duels Marty, the people behind him differ between shots. In the shot outside, there's a tall man with a blue shirt, a young guy and a man with a white shirt. From the angle shot inside the bar, the number of people behind the group has doubled, the man in white is gone and a woman has magically appeared standing next to the man with the blue shirt.
Continuity mistake: After the modern train destroys the DeLorean, Marty lays on the grass, face down. Then, in a close-up, he turns around to watch the train. When the angle changes he is still facing down and crawling on the grass. In the following shot he has moved 5 meters to the right and is sitting by the bushes close to the tracks.