Continuity mistake: As Doc is driving out of town near the end, he stops to help Mary, who is having a difficult birth inside the family station wagon. Doc backs up and parks his car, the front-end is partially across road. While he assists with the birth, a large truck is fast-approaching, only Doc's car is now sitting all the way across the road when it gets hit.
Continuity mistake: In the scene at the diner, where the Mayor and the City Council are trying to talk Michael J. Fox into becoming the town's replacement doctor, watch for the disappearing/reappearing ketchup bottle as the camera angle changes. Several other items on the table move around as well.