Continuity mistake: When wedding has been just called off, Lunch Lady Doris calls everyone for wedding cake, and among people who rush to it we can see Moe (you can recognize him by his eyepatch), then, Lisa starts to walk off and among the people she passes by you can see both Lunch Lady Doris and Moe.
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: The vehicle they are driving changes form when they drop off Bart at military school to when they drive home. They leave with Homer's purple car (obvious from the crumpled headlight) and as they leave the military school it's Marge's orange car (obvious from the ski racks and lack of a trunk). It's clear from the entire scene that this is all one trip.
Continuity mistake: When, Lisa bangs on the window of the operating theatre, there is a person sitting behind her who is asleep. However, when she shouts to Dr Nick, the people behind her are completely different. Then she sits down again, and the sleeping person is behind her.
Continuity mistake: When Homer and Bart are escaping from the cops after stealing kegs of beer from the dump, they drive through a cemetery and slam into a headstone, breaking the right headlight of the car. When they pull into the driveway back at Evergreen Terrace, the left headlight is the broken one.
Continuity mistake: As the Simpsons are in the cinema watching "Kosovo Autumn" you can see there is a seat next to Homer to the right of screen. When Homer starts complaining about the film but cannot leave because he is stuck in his seat, the shot changes and we see him from behind however the seat that was next to him has disappeared.