Continuity mistake: In the opening scene the camera pulls back from a bedside locker to an over the shoulder shot of Kathleen Turner's character doing her make up in the mirror. Close inspection shows that the shoulder in the foreground is actually that of a double who doesn't quite match Turner's movements.
Revealing mistake: Last scene in the movie is Peggy Sue waking up in the hospital. The very last shot of that scene is of the camera backing up from what appears to be a mirror. If you look closely, it isn't a mirror at all, it's actually a window made to look like a mirror complete with another set of actors to mimic the stars of the movie's actions.
Continuity mistake: When Peggy Sue passes out at her reunion, the first shot (from her perspective) is her on the floor, looking up at her daughter and Charlie standing about 6 feet away. The second shot is her daughter and Charlie crouching down close to Peggy Sue's face. In the third shot, Charlie is instantly standing 6 feet away again.
Factual error: Charlie's 58 Impala is a sweet ride, but his license plates don't have the requisite year stickers. His car has the '56 series of plates, and each subsequent year would require that current year's sticker.