Continuity mistake: When Homer says, "You can't take our donuts," his hat is red. But in the next shot and in every other shot of Homer, his hat is blue. This is pointed out on the audio commentary on the Season 4 DVD. (00:12:35)
Continuity mistake: When Bart skates towards Homer's car, attempting to skate over it, the distance between the car and Bart changes between shots. (00:11:00)
Audio problem: When Bart is attempting to skate over Homer's car with his friends watching, Milhouse says 'You're crazy Bart.' but his mouth never moves. (00:10:55)
Continuity mistake: When George and Homer burst out of the manhole, there is a shot of the Simpsons' house covered in mud, then a quick one of it totally clean, then another when it's muddy again.
Raging Abe Simpson and His Grumbling Grandson in 'The Curse of the Flying Hellfish' - S7-E22
Continuity mistake: Grampa loses his red slipper as he is pulled by Mr. Burns' boat. Later it is back on his foot.
Continuity mistake: When the garbage man is asking Homer if he learned anything from love day, his cigarette is in his hand, but in the next shot when Homer says, "That was yesterday moron", the cigarette is now in his mouth.
Continuity mistake: Marge tells Bart not feed Maggie the Monopoly houses. Bart shows the box and says that there's enough of them. The shot later, the box has disappeared. (00:16:15)
Much Apu About Nothing - S7-E23
Continuity mistake: When Barney is tranquilised, he falls with his mouth closed. In the following shots, it's open, closed, then open again.
Continuity mistake: During the "We Do" song, there is a character at the top of the screen who keeps changing colour. I think it might be Dr Hibbert, but his skin colour keeps flickering to yellow.
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: When we first see the book-reading Ms.Krabbapple is sitting at the end of the row. The next time, Groundskeeper Willie is there. And the third time we see the audience, Apu has appeared in The Front row as well. (00:02:25)
Missionary: Impossible - S11-E15
Continuity mistake: This mistake happens twice in the episode. At first, when Homer arrives on the island, he gives the islanders some bibles and says "Knock yourself out." Ack says that they cannot read. Yet later when Homer is revealing the casino, Ack reads "The Lucky Savage-?"
Suggested correction: Homer had been there for a while when the casino had finished construction. He could have taught Ack to read.
'Tis the Fifteenth Season - S15-E7
Continuity mistake: After the family discover the astrolobe, the gift tag disappears from its wrapping. (00:07:25)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Carl complains that he can't be fired, everybody behind him, Homer and Lenny has disappeared. (00:09:00)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: As Horst and the guy talks to Homer, the guy is holding a folder in the first shot, then it suddenly disappears, before appearing on the desk without him putting it there. (00:12:45)
Lisa's Pony - S3-E8
Continuity mistake: When Lisa calls Homer at work, Homer picks up the phone on his left side. Instantly after, we see him hang the phone up on his right side. (00:19:00)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: After Lisa declares world peace, when the two UN guys hug each other, the United Nations symbol on the wall has changed from purple to blue. (00:05:25)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Homer picks up the monkey's paw for the first time, a person walks behind him. He has disappeared in the next shot. (00:02:35)
Continuity mistake: When Bart is trying to get the toilet water to flow the other way, the toilet can't refill that quickly with that number of flushes.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Marge is shopping at the Kwik-E-Mart she puts a red can and a blue can on the counter.When Apu tells her about the offer on hair dye he puts two blue cans into the paper bag.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Audio problem: When Homer is putting Christmas lights around the outside of the house, he falls from the roof. You can then hear Lisa and Bart sarcastically clap. But you can see they both have their hands by their side, and no-one is clapping. (00:04:55)