The Trouble With Trillions - S9-E20
Deliberate mistake: When Homer is being interrogated by the IRS, his package is briefly replaced by a ball of string when the IRS agent sits down in the chair and spins around.
Marge Simpson in 'Screaming Yellow Honkers' - S10-E15
Deliberate mistake: When Marge goes offroading to get home there is a grassy field which leads right up into the Simpson driveway. However, in all other episodes there is no grassy field and instead there is a house in the spot where the field would be.
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Deliberate mistake: In "Clown Without Pity", when the Krusty doll accidentally knocks the head off of Lisa's Malibu Stacy (her doll), Krusty puts it back on but you don't see a crack where the head came off. (00:07:40)
Deliberate mistake: When Bart is in the genius school, the teacher asks him if he knows what happens if he adds an acid to a base. He replies yes, adds them anyway and the lab explodes and a green goo comes out, turning Bart green. If you add an acid to a base, you just get salt and water.
I, (Annoyed Grunt)-bot - S15-E9
Deliberate mistake: When the giant gold robot picks up the robot containing Homer and shakes him, Maggie suddenly pops up from nowhere and bounces around along with Homer.
Deliberate mistake: When Homer is watching Weird Al's parody of his song, he never turns the t.v. on and it isn't already on, but somehow it turns on.
Deliberate mistake: When Homer pushes the trampoline off the cliff, there is no rock below the falling trampoline. However, in the shot at the bottom a tall rock is visible which was drawn there on purpose for the trampoline to bounce off of, despite not being visible in the first shot.
Deliberate mistake: The mouth on the panda costume is in a constant smile and at no point does Homer change it, even when he is in pain. However, when he is being pulled back under the curtain the mouth is open and the mask has a frightened expression. I suppose this was done on purpose, but it's still a continuity error of sorts.
Homer Alone - S3-E15
Deliberate mistake: Arnie says that he drops his bagel. When he does he starts to say it, but when we see the helicopter it has just fallen out. If he dropped it at the time he did, then it would be much further down and wouldn't be visible in that shot. (00:05:20)
Special Edna (a.k.a. Love and Marking) - S14-E7
Deliberate mistake: When Bart and Edna are watching "Holes" in the IMAX theater, Edna sighs and pulls out a locket which we can see the back of. After opening it up to reveal pictures of her and Seymour, we find out its actually a triptych when she opens up another image of Seymour's mother. From the way she unfolds this extra picture, Seymour's mother would have had to be facing outwards, but in the previous shot the back of the locket was blank.
Gump Roast - S13-E17
Deliberate mistake: Where do the "professional roasters" get those home movies of Homer's stupidity? No one could possibly have filmed his skiing mishap or the Funzo incident. Also, how does Maggie keep a mental record of celebrities that she didn't meet in person?
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Deliberate mistake: In "Dial Z For Zombies", Homer is shooting zombies with the shotgun at the school. When he shoots the first two he just shoots them twice. Every other zombie he shoots requires him to slide the gun. It doesn't when he shoots the first couple of zombies. (00:19:50)
Kill the Alligator and Run - S11-E19
Deliberate mistake: When Marge is sweet talking the sheriff, Bart unlocks all but Homer's foot chains, but when they're running for the gate, Marge, Bart, and Lisa's shackles can be seen.
Deliberate mistake: Lou and Eddie are driving Bart around in the cop car. Bart asks when they're going to shoot people. The shot cuts to Lou, who is driving. The entire frame of the car disappears around him and it's just him superimposed over a background. The shot cuts again and the frame is now visible. Even if it was a low-angle shot, you'd still see the roof of the car.
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious - S8-E13
Deliberate mistake: During the final musical number, just after Marge sings "I'm going bald from stress," the family sings "But we're happy just the way we are," but Homer's mouth doesn't move, because the producers forgot to record Dan Castellaneta's lines.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.