Continuity mistake: When Mr. Burns pushes the child on the swings, he somehow manages to defy the laws of physics. When he pushes the child forward for the last time, he swings forward, then back, hitting Mr. Burns in the head. He then swings forward again, hitting Mr. Burns from behind. Mr Burns starts saying "You've won this round..." and the child then hits Mr. Burns from behind again. In order for this to happen, he would have to go completely around between the second and third hits and you clearly see he doesn't.
Lisa on Ice - S6-E8
Factual error: The clock in a hockey game does not run during a penalty shot.
Continuity mistake: When Lisa is with Apu, Paul and Linda the wall behind her is purple.On a close up of her when she's listening to Apu it's blue.In the next shot it's purple again.
Springfield Connection - S6-E23
Continuity mistake: When Marge is in the supermarket, she only has about 4 items in the trolley. But just before the trolley crashes into the cheese model, it is full.
Continuity mistake: The coathanger is too small to reach the medicine cabinet.
Radio Bart - S3-E13
Continuity mistake: In the scene where Bart tries to get his radio back from the well, watch the police barriers. When Lou and Eddie get coffee, they walk through one of the barriers, tearing it. Several shots later, this torn piece has vanished, and then the barriers disappear entirely. (00:15:40)
Continuity mistake: When Moe tries the Flaming Homer, there are bottles that keep appearing, and the knife disappears suddenly. (00:06:55)
Continuity mistake: Before the time trials start, the audience on the sidelines keep disappearing and reappearing. (00:12:30 - 00:13:40)
Like Father, Like Klown - S3-E6
Other mistake: At the very end, when Krusty's father throws the pie in his face, the food instantly comes off his face. (00:21:40)
Continuity mistake: When Otto announces about Milhouse's party, 1, Martin is sitting two seats ahead of Bart and Milhouse, even though he was just talking to them, and 2, Sherri and Terri are nowhere to be seen. (00:01:35 - 00:02:35)
Continuity mistake: When Bart realizes he forgot his permission slip, the camera shows us that the paper is half-under his pillow. However, when he got out of his bed at the very beginning, the paper wasn't under his pillow. (00:01:00 - 00:03:05)
Continuity mistake: When Lisa is clapping erasers because she sassed Miss Hoover a second time, the room's clock is visible near the top of the ceiling. However, the clock wasn't there several shots earlier. (00:17:00)
Continuity mistake: At the end of the episode when Mr. Burns rotates his desk to turn off the power, the ink block and fountain pen to his left change position.
Continuity mistake: When everybody is chanting 'Film Festival', you can see that Mayor Quimby has his arm up. But in the next shot, which changes so that you can see Marge, he his holding up his other arm.
Continuity mistake: During the lamb vision at dinner Lisa is holding her knife and fork. In the very next shot they're on the table.
Continuity mistake: When Sadgasm is making their first appearance, Homer says, "We are Sadgasm," and there are a few students walking around, but when he says, "And this song is called 'Politically INcorrect'," there is a big crowd in front of them with no time to form one.
Miracle on Evergreen Terrace - S9-E10
Continuity mistake: When Bart pulls the melted tree out of the house, a shovel appears out of thin air so he can shovel snow onto it.
Lisa's Rival - S6-E2
Continuity mistake: When Nelson does his "Grapes of Wrath" demonstration, it splatters all over Skinner's jacket. When he walks over to the rest of the dioramas his jacket is clean again.
Homer's Barbershop Quartet - S5-E1
Audio problem: When grandpa is listening to the radio, he says something like 'oh.', but his lips are not moving.
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.