Continuity mistake: John is wearing Homer's old "Pin-pals" bowling shirt when the Simpsons first meet him, but only after we see the back of the shirt does the name "Homer" appear over John's breast-pocket; clearly there was nothing there during their entire previous conversation. And even if this is a deliberate "mistake" for comic purposes, in 7th season episode"Team Homer", the very same bowling shirt is ripped to shreds when Homer is being mauled by Mr.Burns' dogs at the very end.
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.
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. (00:07:00)
Continuity mistake: In the episode which recalls how Homer and Marge got married, Homer writes a note to Marge on a piece of paper entitled 'From The Pen Of Patty' he SCRIBBLES out Patty's name and writes his own, but when Marge reads the note, 'Patty' only has a single straight line through it. The word "HOMER" also changes.
Continuity mistake: Springy the Olympic spring that Homer makes has 9 coils. Then we see the large version that has many coils, at the Olympics meeting. Homer's original spring is in his hand and now it has many coils also. When it cuts back to the stage, the large spring has few coils, like the very first time we saw Springy.
Continuity mistake: When the Simpsons are eating and the family are praising Marge, Homer's plate is first seen to have a small amount of yellow food and a bit of pink food (meat?).In a later shot when Homer steals and uses Marge's pepper spray he has a large pile of yellow food.