Continuity mistake: When Marge's sisters start smoking in the flashback, there is only one ledge on the wall behind them. In the next shot there are three ledges and a clock. (00:04:05)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Homer drives his normal car to the plant's parking lot. When he and Carl meet, his car has changed to being blue. (00:07:00)
Lisa's Pony - S3-E8
Continuity mistake: During Lisa's performance, In one shot of the audience we see, from left to right: Ned Flanders, Maude Flanders and some lady. The rest of the talent show showed us that Jasper was sitting where the lady was. (00:05:45)
Continuity mistake: When Lisa first discovers Jebadiah's confession, she is holding the fyffe and wearing his racoon hat, the screen fades to black (I'm guessing for the ad break) but when it comes back Lisa is standing in exactly the same position, still reading the confession, still holding the fyffe, but no longer wearing the hat.
Continuity mistake: There are two problems with Lisa's Indian burns. When we first see them, she has 4 burns. Then, while she is showing them to the bullies, there are 3, then 4 again. Then, in the very next scene when she is walking with Nelson in the schoolyard, they are gone altogether.
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When there is a queue to see the movie, it stretches right back to the Simpson house, and we see Bart looking through the window. However, when Homer talks to Bart whilst sitting on the window, the queue has disappeared. (00:16:45)
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When the Simpsons are about to eat on the spaceship, in one shot just before they eat there are 3 candles on the table, and when they all sit down they're gone. (00:10:40)
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: Just before Duff man arrives, Barney has loads of sweat on his shirt. But when Duff man pushes the big jug of beer towards him in the next shot, the sweat is gone.
Continuity mistake: When we see Skinner's car before the newspapers fall on him, it is a light-brownish color. When the police arrive, it is the same color as the cop cars. (00:19:10)
The Secret War of Lisa Simpson - S8-E25
Continuity mistake: The vehicle they are driving changes form when they drop off Bart at military school to when they drive home. They leave with Homer's purple car (obvious from the crumpled headlight) and as they leave the military school it's Marge's orange car (obvious from the ski racks and lack of a trunk). It's clear from the entire scene that this is all one trip.
The Trouble With Trillions - S9-E20
Continuity mistake: When Homer is watching TV early in the episode, he has a watch on his left wrist. When he begins working on filling out his tax forms, the watch has disappeared. When he takes down the sailboat painting from the wall, the watch has returned.
Continuity mistake: When Marge and Homer are put in stocks, Marge initially has lipstick on, but in subsequent courtroom scenes it has disappeared.
Continuity mistake: At the end of the Capital City number, where the car comes towards camera before they shout "Capital City, yeah", watch Marge's dress. It's green as the car approaches, but as soon as it parks, it turns red, right before your eyes.
Bart vs. Lisa vs. the Third Grade - S14-E3
Continuity mistake: When we first see Willie standing by the Black Wall of field trips, the latest entry is at Willie's eye level. But when the angle changes, there are a lot more names on the wall, making the last entry appear just by Willie's chest.
Continuity mistake: The stocks that are put on Marge and Homer are fitted so that their head and hands are secured and cannot be removed. Whilst in Flanders garage and Homer is using the rotary saw to remove Marge's stock, Homer's stock is still secured on him but his arms and shoulders are through the stocks.
Continuity mistake: When Homer and Marge are on stage with Brad Goodman, Homer is eating toffee apples. He keeps eating them but they stay the same size.
Fat Man and Little Boy - S16-E5
Continuity mistake: During the scene when the toys are talking about insurance, the design on the arm of the blue jacket changes in different shots. (00:04:00)
Continuity mistake: At the beginning of the episode, the school is a light purple colour, yet near the middle of the episode, the school turns yellow. (00:00:50 - 00:12:20)
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: During both conversations Lisa has with the real Stacy (the creator of Malibu Stacy), her drink magically refills itself a number of times.
Catch 'em If You Can - S15-E18
Continuity mistake: When Bart, Lisa, Homer and Marge are on the ferris wheel near the end, we can see in one shot the person behind Lisa has blonde hair, and then in the next shot the person has black. (00:18:45)