Continuity mistake: When Marge talks to cable guy, the trees and hammock disappear.
Continuity mistake: In class, when Lisa is sitting at her desk, pondering the Jebadiah mystery, her tray of cookies and glass of milk is very visible. Then when Lisa says "The missing piece of the puzzle. I've got it." and runs out of class, the cookies and milk are no longer there.

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: In the scene where Selma and Troy McLure get caught by the press outside the resturant, Selma and Troy swap places between shots.
Continuity mistake: When Bart is looking for candy in the cupboards, the wine bottles in the nearby rack change position between shots.

Continuity mistake: In the scene where Homer dodges the cannon ball, he is wearing goggles and a helmet. But when Homer jumps down from the platform and hugs Marge, his helmet and goggles have disappeared.
Sideshow Bob's Last Gleaming - S7-E9
Character mistake: Homer drinks 6 non-alcohol Duff at the air show, but is charged for 8.
Continuity mistake: Homer opens the door on Bart just before he shows the kids his BBQ invites but there is never a door there in the Simpsons' home, only a doorway.
Continuity mistake: When Marge puts more lamb chops on Lisa's plate they are now grey in colour. Also the ones already on her plate have turned to grey.
Continuity mistake: The moss on Walt Whitman's grave when Homer removes it changes.
Much Apu About Nothing - S7-E23
Continuity mistake: When Willy is threatening the children and Skinner it shows that Lisa has her hands on her sides and she is holding nothing. In the following shots, she has a blue book held against her chest.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob return to Quimby his assistant's clipboard changes colour between shots.It goes from light brown to burgundy then back to light brown again.
The Simpson's 138th Show Spectacular - S7-E10
Continuity mistake: During the false ending to "Who Shot Mr. Burns: Part 2", Smithers moves position when Burns explains what happened.
Continuity mistake: The antenna from Homer's car disappears when he drops Mother Simpson at the gas station.
Continuity mistake: When Homer is showing his BBQ invites to the kids Bart comes and stands next to Lisa and points to the extra 'B'. In the next shot, he's back over near Homer.

Home Sweet Home-Dum-Diddly Doodly - S7-E3
Continuity mistake: At the Flanders' house, in the kitchen, Bart and Lisa have sandwiches on plates in front of them. The shot changes and everyone on the table has an empty bowl including Bart and Lisa.
Who Shot Mr. Burns? (2) - S7-E1
Factual error: When Chief Wiggum opens the revolver's chamber, there's 5 rounds with one open slot. In the next shot, we see the reverse end of the chamber and it's drawn in such a way to indicate those 5 rounds all have bullets in them still, meaning the empty slot is from when Maggie shot Mr. Burns. But revolvers don't eject spent shells automatically and no one handled the gun after it dropped on the floor. So the empty casing should have still been in there when Wiggum opens it up for the first time.
Who Shot Mr. Burns? (2) - S7-E1
Character mistake: Willie says he got arthritis from playing Space Invaders in 1977. However, Space Invaders didn't come out until 1978.
Sideshow Bob's Last Gleaming - S7-E9
Factual error: Sideshow Bob couldn't hide out in the Duff blimp's helium pocket because there wouldn't be any oxygen.
Team Homer - S7-E12
Continuity mistake: When Moe says Mr. Burns is going to have an accident, he's wearing his pin pals shirt. When Moe hits Mr. Burns, he wears a mask and different clothes. Moments later, when talking to his bowling team again, he's back in his pin pals shirt.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.