Fat Man and Little Boy - S16-E5
Continuity mistake: When Bart is playing with his toys, we see that in one shot on the shelf there are 4 books, then in the next shot there are 5. (00:03:50)
Continuity mistake: When Bart attempts to skate over Homer's car, his three mates are watching. Between shots they change from standing on the driveway to standing on the pavement. (00:10:55)
Continuity mistake: Wiggum asks Homer for another burger and Homer throws it to him. When he catches it Otto has disappeared from sitting next to Eddie.
Much Apu About Nothing - S7-E23
Continuity mistake: In the final high-up shot of the Simpson's garden with everyone chanting 'No on 24'; Lisa has disappeared from next to Apu, and Ned Flanders' glasses have vanished.
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: After Maggie makes her wish, the family jumps from being in their seats to beside the window. (00:03:50)
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Marge is on the phone to her sisters, her necklace changes from white to red.
Continuity mistake: At the beginning, when we see the exterior shot of the bus, it is full of kids. In the interior shots, 1) before the twins talk to Bart and Milhouse, every seat is empty, even Sherri and Terri's. 2) when the bus arrives at the school, we AGAIN see a full busload of kids. (00:01:30 - 00:02:25)
Continuity mistake: Marge said to Bart she would make Butterscotch chicken for him, but in the Season 2 episode "Blood Feud" Marge says Bart's allergic to butterscotch.
Continuity mistake: When Homer is sitting in the Frying Dutchman with the crowd gathered round looking at him, the Captain invites people in. Some start walking in, but in the next shot where they are all gathered round again, it is the same group of people again. (00:17:00)
Pygmoelian - S11-E16
Continuity mistake: At the start of the episode, Homer wakes the family up and they get in the car in their night clothes. When they arrive at the destination, they are dressed.
Continuity mistake: After Selma gives Madam Wu the sack of ten thousand "happinesses" the sack instantly vanishes from off the table. (00:08:40)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Jimbo and Kearney take Homer's candy, it is obviously night time. However if you watch the outside as Homer closes the door before he says "Lousy punks" it shows a daytime sky.
Continuity mistake: After Bart and Milhouse drink the all-syrup squishee, the syrup disappears from Bart's face between shots.
Burns' Heir - S5-E18
Continuity mistake: When Smithers finds Burns drowning in the bathtub, he throws the rag. When the rag hits the floor, it magically disappears.
Continuity mistake: When Homer is taking the kids to school for the second time the view behind him doesn't look further away while driving.
Brake My Wife, Please - S14-E20
Continuity mistake: When Hibbert handcuffs Bart to the radiator, for one brief second, his cast and bandages disappear. They return in the next shot.
Sweets and Sour Marge - S13-E8
Continuity mistake: When Homer falls off the human pyramid, he grabs onto someones rear end to stop himself from falling. In the next shot, he is suddenly holding a foot.
Continuity mistake: When Homer opens the door on Bart the door handle is purple with a grey backing. Later when Homer is saying 'If I went to a BBQ and there's no meat...' there is only the purple knob.
Continuity mistake: When Lisa is standing outside the Kwik-E-Mart, the "open 24 hours" sign on the window changes position between shots. (00:13:00)