Continuity mistake: In the scene where Marge is talking to Bart's teacher, Marge is "punished" by writing lines on the blackboard. In the first shot of her doing so she has written the line 9 times, but in the next shot there are 11 lines. (00:05:10)
Continuity mistake: When Marge and Homer are at the Springfield formal ball at the Country Club, about half way through the ball, there is a woman with her back to the camera as she is talking to Marge and Homer. Homer is on Marge's left side. In the next shot when Marge's back is to the camera and you can see Marge still talking to the woman, Homer is no longer on Marge's left side, he is gone.
Continuity mistake: Bart is shown sitting tied up on the couch and Ms. Botz walks in carrying a tied-up Lisa in her arms before dumping her on the sofa alongside Bart. You can see that the rope Ms. Botz has used to bind Lisa is wound right around her body from the neck right down to her ankles. A few shots later when Maggie comes down and frees her, the rope tying Lisa's legs together at the knees has disappeared.
Continuity mistake: When Bart is in the ice cream parlor breaking up with Greta, the waiter tells him "We get that a lot around here" and point over to Chief Wiggum and Lou sitting behind and to the left of Bart. Bart turns his head all the way to the side to see them. The focus then goes to Chief Wiggum and Lou, but when their part is done and the "camera" goes back to Bart and Greta, the policemen are sitting behind and to the right of Greta, so that Bart would not have had to turn his head to see them.
Continuity mistake: Whilst Chalmers notices the Honda symbol missing from his car, there are four holes in the corners of the leftover symbol. There is a screw in one of the holes indicating the symbol would have holes in its corners to hold it down. Later when Skinner finds the Honda symbol in Nelson's locker you can see there are no holes in the symbol.