Continuity mistake: The right handle plate on Homer's gun is fastened with two screws throughout the entire episode. But in the scene where he promises Marge to get rid of the gun and they hug in the kitchen, the gun is seen lying on the table with only one screw in the handle.
Continuity mistake: When Bart crashes at the social club, his skateboard changes position between shots. (00:05:30)
Continuity mistake: When Bart hands Ms.Krabbappel his final test, there are some shots going back and forth between their faces. During the first shot looking at Ms.Krabbappel, you can see a window behind her, and outside the window, there is no snow, even though there was a whole lot of it yesterday. During the next shot, the snow IS there. As the camera goes back and forth, the snow disappears and reappears.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Homer gets thrown out of the house by Marge and Otto walks up to him, you can see that it is Smithers and Carl standing behind Homer. Yet in the next shot when you see Homer's face, it is now Principal Skinner and Carl standing there.
Lisa's Pony - S3-E8
Continuity mistake: At the very end, the outside of the Kwik-E-Mart is different. (00:21:35)
Audio problem: After Homer and Marge steal Gil's balloon, they fly towards clothes, Marge says "Clothes! We're saved!", but her mouth dosen't move.
Burns' Heir - S5-E18
Continuity mistake: When Homer and Marge are talking to Chief Wiggum, the Rubik's Cube and the cup on his desk changes to a doughnut between shots. (00:13:20)
Homer Badman - S6-E9
Character mistake: When Grandpa is putting up the American flag for Homer's public access show and Marge says the flag only has 49 stars, there are actually only 38: 8+7+8+7+8.
And Maggie Makes Three - S6-E13
Plot hole: When Homer is seen at work in the flashbacks (before Maggie was born), he is at his usual control panel in sector 7-G, but he only began working here when Burns made him safety supervisor in season 1, "Homer's Odyssey". Before Maggie was born he should have been working at the conveyor belt with the carbon rods, where we saw him in the first couple of episodes.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer finds out that he has no Christmas bonus the background behind Marge is the kitchen, but then it cuts to Homer and the background behind him is the kitchen too. (00:08:20)
Continuity mistake: When the cops pin Krusty to the carpet, he moves further away from the yellow stripes between shots.
Other mistake: When Homer and Chief Wiggum fall into the waste, in the second shot, the cliff edge looks very weird. It seems to be transparent with Ruth's car floating in mid-air, and there is a big curved wall that doesn't have ground at the top.
Kill the Alligator and Run - S11-E19
Continuity mistake: When Homer beats the train they are on a road, but then another train comes by and hits them right where the road was.
Revealing mistake: When everybody is in a big fight at the Do What You Feel Festival, watch out for a man in an orange shirt with black hair. His left eye keeps disappearing for one frame.
Continuity mistake: When Bart's army is attacking Nelson, there are a lot more kids attacking Nelson than there were training with Bart.
Continuity mistake: When the remote controlled plane crashes into the roof of the burlesque house, it is seen to hit only the side of the roof, yet when Bart goes to reclaim the plane, it is nested on the top of the roof.
New Kids on the Blecch - S12-E14
Continuity mistake: When Homer is pinching Lisa with the "jealousy bug", the sign behind him changes from a gift store to an antique store.
Continuity mistake: When Marge is watching Homer's "Margarine" music video, the coffee in her cup keeps changing.
Continuity mistake: When Homer sits down in the movie theater, all the rows are completely full, including the row behind him. When he turns around to talk to Selma, the seats directly behind him are empty. Then, when Homer turns back to the screen, the Sea Captain and Dr. Hibbert appear sitting directly behind him.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.