Homer vs. Lisa and the 8th Commandment - S2-E13
Revealing mistake: When Homer is imagining being locked in the jail cell and he turns around to find he is in his own home, he turns to look at his family. There is a close up shot of his terrified face, and the people in the background watching the game (I think it might be Lenny and Carl) have no eyes. The rest of their face is fine, but their eyes are missing.
Revealing mistake: When Lisa is explaining to the curator of the museum why she didn't tell the crowd of what she learned about Jebediah Springfield, if you look in the background none of the people on the far sidewalk are moving, almost frozen in place with some of them with their arms in the air yet everyone and everything in the parade keeps moving right along.
Revealing mistake: If you look carefully in Mr. Burns' surveillance cameras, the workers are identical. (00:02:50)
Bart's Friend Falls in Love - S3-E23
Revealing mistake: When Bart tells Otto not to leave due to Milhouse not being on the bus, when Otto replies you can see that his left arm up to the headphone cable flashes pink for a frame. (00:07:45)
The Last Temptation of Homer - S5-E9
Revealing mistake: Just before Homer drives backwards into the trout hatchery, when Homer turns the key it is obvious that it is repeated footage of Marge turning the key because the hand is a lot thinner.
Revealing mistake: After Apu and Manjula go by in horse and cart everyone returns into Moe's. When they walk in they just disappear into a brown wall which is where the inside of Moe's should be seen.
The War of the Simpsons - S2-E20
Revealing mistake: When Ned says "Crème de cassis" while describing what was in the drink he made. There are several animation errors in this shot. His head is disconnected from his body, and his nose disappears. Also, a part of his face is missing between his fingers while he does the 'OK' hand gesture.
Lisa vs. Malibu Stacy - S5-E14
Revealing mistake: When Lisa says "Now all we need is a name", Maggie's head disappears for a split second right before the shot changes to Bart talking. (00:17:20)
Revealing mistake: When Marge says, "Slow and steady wins the race", her face and body are two different colors.
Revealing mistake: When Lisa is clapping erasers, you can see the alphabet above the board, and part of the A is cut off.
Last Exit to Springfield - S4-E17
Revealing mistake: When we see Lisa singing and playing the guitar for the second time, if you look to the right you can see a blue mark on the building that is behind her (On the middle turquoise stripe). It appears and disappears twice.
Revealing mistake: When Lisa is daydreaming about her failed test, the president of Harvard talks to her. When he says, "Nasty business that zero", his right white sleeve turns the same color as the glass above the door.
Revealing mistake: When Lisa and Hugh go by Taxi to the Simpsons house, you can see that they pass the same buildings all the time, especially "Coffee shop".
Revealing mistake: In the scene where Marge is cutting Grampa's hair, his left cheek in the mirror's reflection turns blue.
Revealing mistake: When Moe and Barney are seen drinking wine at the wedding, somebody walks away with a tray. When they are drinking the animation is repeated because you can see part of the tray keeps coming on and off-screen. (Look by the bottom right). (00:13:25)
Revealing mistake: When the announcer says that the Falcons win, he says "Who would've thunk it" Homer says "My daughter, that's who". When he is saying this, Lisa's arm disappears twice. (00:10:05)
E-I-E-I-(Annoyed Grunt) - S11-E5
Revealing mistake: After Lisa says "For a product that's evil and deadly" while standing in front of the tomacco stand, there's a duplicate Lisa behind her that stands still while she moves, giving Lisa the appearance of having two heads. It looks like the animators made a mistake while trying to animate Lisa.
I'm Goin' to Praiseland - S12-E19
Revealing mistake: In one of the scenes (I think it is when they first discover the alleged 'miracle') you can see people in the background walking out of the park. But they are not walking out of the park at all, they are walking into the wall.
Springfield Connection - S6-E23
Revealing mistake: Just after when Marge is reading the book on the sofa she says 'chaos'. On the far left of the screen a large black 'scratch' appears then just slides off.
Revealing mistake: When the riot police are running into the concert, you can see a 'cardboard' police officer leaning against his car, doing absolutly nothing, not even blinking or talking into his police microphone. (00:07:45)
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.