Continuity mistake: After Kirk (Milhouse's dad) drives away from the stadium, Bart and Homer are walking along and you can see the Drink Duff sign right next to the edge of the fence. The next shot of Homer noticing the sign, the sign is further away from the edge of the fence and is smaller.
Continuity mistake: When Homer and Sideshow Bob are chasing the mechanic on stilts, the mechanic tries to get away, and his cape falls off while he is being chased. In the next shot, we see a close-up of the mechanic, and you can see his red cape is back on again. Then in the next shot, we see Homer and Bob chasing him, and his cape is off.
Factual error: During the video screening at the Teacher of the Year committee, the panel is watching the teacher who acts like Robin Williams. In the video the main judge says "Next" and pushes a button on the video control. It goes to the video that Bart Simpson sent in. How was this possible? The video control would only fast forward the video and two separate entries would not be sent in on the same tape. The committee wouldn't have spliced the footage together onto the same tape as the tapes were piled up on the desk. At the start of the scene one of the judges mentions to put in the next tape.
Other mistake: Bart and Lisa overload the nuclear power plant to create a city-wide blackout so everyone can see the meteor shower. All the lights in Springfield blow out. Yet when we see the Simpsons sitting on their lawn watching the shower, every single window in their house is yellow, as if every room has their lights on. It is the only house shown with power.
Continuity mistake: When we first see Willie standing by the Black Wall of field trips, the latest entry is at Willie's eye level. But when the angle changes, there are a lot more names on the wall, making the last entry appear just by Willie's chest.
Continuity mistake: Whilst Moe is talking to himself about going back to barber college the door to his bar is wide open. When the shot changes to him when he says "Who the hell am I talking to?" the door has suddenly closed. There was not enough time for it to close between shots.