Deliberate mistake: When the boy jumps on the Police motor tricycle and his father jumps on as pillion passenger it is obvious in the subsequent scenes that a small but adult stand-in is riding the trike.
Factual error: When Judge Reinhold is in the department store playing the Space Invaders video game, and one of the men chasing the skull comes to talk to him, Judge continues to play the game, so the man stands between him and the screen in order to get his full attention. If you watch the screen, the game actually continues to play on.
Continuity mistake: Fred Savage (the young boy but with his father 'inside' him) stays with his father (Judge Reinhold) who has his son 'inside' him. Just before his mother walks in he has a glass of Vermouth with some olives in his hand. The glass is half full. He walks into the bathroom. When he returns and his mother arrives and sees him DRINKING, the glass is full.