Continuity mistake: The seating arrangements during the Cheech and Chong show keep changing between shots. Smithers is first seen sitting between Patty and Luigi, then he is between Louie and Legs, and then he is between Patty and Luigi again, then finally, he is sitting next to Mr Burns. And Miss Hoover is at first two rows in front of the Simpsons, then she is a row behind them when Homer is going to the stage.
Continuity mistake: When Roger Meyers throws his nameplate at the writer the second time, the animation is repeated from when he threw it at him earlier. It's more obvious because his mouth doesn't match what he's saying and the background is orange instead of purple like the rest of the scene.
Revealing mistake: The shot of Homer saying "Marge, when kids say bad these days, they mean good. And to shake your booty means to wiggle one's butt" is recycled from the opening scene from Life on the Fast Lane. Notice the animation is of a much lower standard than the rest of the episode.
Audio problem: In "Clown Without Pity" when Homer yells "The doll is trying to kill me, and the toaster's been laughing at me!" his mouth doesn't move.