Continuity mistake: In the second segment of "Treehouse of Horror XXI," as Roger is telling them about what happened to him, as he finishes the story of Marge and Homer saving him, in his recount Marge is wearing a shirt and bikini bottoms (the shirt is covering the bikini bra). But when they saved her, she was just wearing a bikini.
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: Mr. Burns attempts to plan revenge on Springfield by placing the town in a dome. However when Lenny tells Burns it has already been done, Mr. Burns tells the helicopters to stop placing the dome. In this shot, both Burns' helicopter and the helicopters placing the dome are the same height off the ground. But in the following shot, the helicopters are now 50 feet above Burns' helicopter.