Continuity mistake: When Nelson asks Bart what song he is playing as they wait for the bus, Nelson's vest is orange and his shirt is bluish. However, when the bus arrives and Nelson goes to get on the bus his vest is now bluish and his shirt orange.
Tobin OReilly
Tree House of Horror VI - S7-E6
Continuity mistake: During the 'Nightmare on Evergreen Terrace' segment, when Bart is running from Willie, he plans to sink Willie in the sandbox. In the first view of the sandbox it is isolated on a field, yet when Willie is sinking in the sand there is a jungle-gym beside the sandbox. (00:11:35)
Hamster
Continuity mistake: As Bart is forced to show Marge the item (picture frame) he is hiding, he pulls it out of his jacket and he hands it to Marge. As he pulls it out you can see there is nothing in the frame or on the border of the picture frame. After Marge's reaction to the photo we see a close up of the frame and there is now a picture in the frame and some colorful decorations around the frame. Whilst the frame could have been the backside when he pulled it out he never turned it over when handing it to her, and Marge never turned it around when looking at it.
Lummie 
Continuity mistake: When it is announced that Amber is the winner of the contest, and Lisa is runner-up, the stands in the back of the stage are empty. However, when Lisa walks off, all the contestants are back on the stands.
Dandude776 1
Tree House of Horror XII - S13-E1
Continuity mistake: At the end of 'Hex and the City,' there is a shot of the wedding cake, then it pans across the people at the wedding, and you can see Homer with his white shirt on. But then when it goes to a closeup, he suddenly has a blue suit and tie on. (00:06:45 - 00:07:20)
Hamster 
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.
David Mercier
Skinner's Sense of Snow - S12-E8
Continuity mistake: When the Hamster rolls through the glass of Flanders car it breaks it near the bottom middle of The Front windshield. Later on when Flanders and Homer are taking the kids home you can see the break in the glass has now moved to about halfway up The Front windshield. On of the following shots it moves back to its original position and then moves back to being around the middle of the windshield.
Lummie 
Continuity mistake: The colour of the alien poster in the nerds' room changes from pink to blue.
He's My Brother
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)
Yoshi
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: At the beginning, Mr. Burns pats his alligator, and his hand is instantly down in the next shot. (00:01:50)
Yoshi
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Marge reveals the Christmas money from her hair, her necklace changes from red to white. (00:05:30)
Like Father, Like Klown - S3-E6
Continuity mistake: When Bart and Lisa see Reverend Lovejoy, their chairs keep moving closer/separating between shots. (00:13:05)
Yoshi
Continuity mistake: When all the salt spills out onto Milhouse's lunch, the salt that was on his food tray has disappeared. (00:10:50)
Yoshi
Continuity mistake: In the scene where Homer is on stage in Springfield, he's wearing shorts. When he jumps off the stage after dodging the cannon ball, he's wearing pants.
Continuity mistake: At Moe's, when Homer takes hold of the telephone its color is red, but then changes to blue as he speaks to Marge.
Super Grover 
Like Father, Like Klown - S3-E6
Continuity mistake: In Krusty's story after he has his makeup washed off by a rabbi, just after his father speaks to him his makeup suddenly reappears. (00:09:40)
OL1V3R666
Continuity mistake: When the newspapers fall on Skinner, the rake in the corner has turned into a shovel. (00:19:10)
Yoshi
Continuity mistake: After Bart is attacked by the wolf and goes back into class, the banner above the chalkboard that has the alphabet on it is blue. Every time we see the banner after that it is yellow. (00:18:40)
Lummie 
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' the blue button on the toaster occasionally differs from being at the bottom of the lever to suddenly at the top, visible in the first shots of Homer fixing the toaster and between shots after Homer sits on the pink fish. (00:09:25 - 00:12:45)
Hamster 
Continuity mistake: When Homer drives his car to work it is lime green instead of the usual purplish color.
Tobin OReilly
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.