Bart Carny - S9-E12
Continuity mistake: When Cooder comes out of the house to witness Homer throwing the ring onto the chimney, there's a doorbell on the side of the doorway. The next shot, it's disappeared.
Continuity mistake: When Homer is fishing, the colours of the things on his hat switch places between shots.
Continuity mistake: When Frink collapses at the table, his sleeves are green. When it cuts to a wide shot, they are yellow.
Continuity mistake: When Bart and Lisa are in the compound, just before Bart gets brainwashed, the bags that were behind Lisa disappear. Homer and Marge were on the other side of the room, so they couldn't have picked them up.
Bart Carny - S9-E12
Continuity mistake: When Homer is talking through the door to Cooder about getting the house back, the shot is through the fisheye lens on the door and you can see Marge, Bart and Lisa smiling. The very next shot, they suddenly have a frown in no available time.
Gal of Constant Sorrow - S27-E14
Continuity mistake: When Homer returns from work to get the cat out of the plug socket, he removes the plug socket cover without removing any of the plugs, but when Homer realises that the cat is in the ceiling, both the plug socket cover and the plugs have now been removed from the wall.
Continuity mistake: Flanders is seen signing the agreement with his right hand. In later episodes, he is known for being left-handed.
Last Tap Dance in Springfield - S11-E20
Continuity mistake: Milhouse is barefoot when he and Bart discover the lion, but seconds later, when it chases them, he is wearing his shoes again.
Continuity mistake: As Homer begins his improv act, Lisa is seated elbow-to-elbow with Dr. Nick. In the long shot view from the rear, she is much further from Dr. Nick.
Continuity mistake: Lenny and Carl's seating in the auditorium changes from being down close to the stage to being higher up and further from the stage.
Continuity mistake: Before Homer begins his speech to the nuclear power plant employees, Lenny and Carl are wearing white/off white shirts with ties. After the speech, Lenny is wearing his usual green shirt with suspenders and Carl his usual gray jacket.
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: When Roofi is singing at the concert, the Roofi head on the curtain is facing the left. Later, it is facing the right.
Continuity mistake: The colour of the school changes from yellow when Martin and Bart are talking before the test to grey when Bart has spoken to Otto about being held back. (00:07:00 - 00:11:00)
Continuity mistake: When Marge kicks Homer out he turns away from the door. When she slams the door he is now stood facing it completely. (00:12:40)
Continuity mistake: In the title sequence Mr. Largo has a baton in his hand when conducting. This disappears as he stops conducting to throw Lisa out. (00:00:50)
Continuity mistake: At the end, we see Krusty stood next to Mr. Burns. However, as the camera pans over the crowd he has vanished. (00:20:30)
Continuity mistake: Lisa's posture changes at the breakfast table as Bart talks about the school bus. (00:16:10)
Continuity mistake: The position of the street lamp Bart skates into changes between shots. Notice the lines in the pavement. (00:08:20)
Continuity mistake: When the car pulls up by the theatre, you can see it through Bart's window. As the car drives off it's now trees outside his window. (00:08:00)
Continuity mistake: When Marge is telling Homer off about staying in the car she has gloves on. Camera changes to her saying "Move it" and now her glove has disappeared. Her hand also moves from being on the door to pointing. (00:05:00)