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.
Audio problem: When Horst is checking the power plant, he sees some radioactive liquid pouring out of the chimney, he says "That shouldn't be" but his mouth doesn't move when he says "be". When he spots the raccoons he speaks but his mouth does not move at all. And at the end when Mr Burns is mocking the German men, Horst says "Burns, stop it." but his mouth doesn't move.
Other mistake: In the scene where the Simpsons are viewing the path of the Corvair's Re-entry, the blip representing the spaceship crosses the entire US from North-West to South-East in about three seconds. This is really impossible, even for something going as fast as a spaceship on re-entry would be.
Continuity mistake: In the 'Nightmare on Evergreen Terrace' segment, in Bart's dream you see a shadow of what looks like someone with four knife-fingers. Then when we see who it is, it is Willie holding a rake. But the rake has five tines, not four, so the shadow is wrong.
Continuity mistake: When Bart and Lisa are trying to win back Homer's affection they are sitting on the top of the stairs and push the skateboard with the present on it down the stairs. In the next shot it rolls into Homer's legs yet it would be impossible as he was standing in the main living room which is to the right of the stairs. Pushing the present down the stairs it would go straight into the front door.