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.
Factual error: Deer are not repelled by the smell of human urine, and in fact it does not have "a" smell - it has many. The smell of human urine varies enormously based upon diet, health and environmental factors so that no wild animal could possibly be scared of them all. Even if Lou didn't know this (and everything about her character suggests she should), Doctor Stone would - he is a doctor, after all.
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.