Continuity mistake: Just before Marge tries to sell Skinner the tie rack, she is writing on something. She then puts her hands down by her waist, and then brings one up to turn it on and both up to pull the motor out. The point is that the pencil and the item she had in her hands have simply vanished, and we never saw her put them down either.David Mercier
Continuity mistake: When Professor Frink is explaining where Homer is, in "Homer3", Ned Flanders is leaning behind the couch between Bart and Marge, and Chief Wiggum is standing up. When Homer complains, Ned is between Marge and Chief Wiggum, who is now sitting down on the couch.
Continuity mistake: When Bart crashes at the door of the Legitimate Businessman's Social Club, his head is facing the door. You can only see this for several frames. In the next shot, his head is facing the sky. (00:05:25)Yoshi