Continuity mistake: At the bar, we see Mrs. Krabappel, and she disappears for the rest of the scene. (00:13:40)
Continuity mistake: When Skinner is set free, while holding onto the vacuum, he changes position between shots. (00:20:15)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: At the Tavern, when Homer slaps the money on the table, the white cloth that Moe was holding has vanished. (00:04:55)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Before Horst wants to talk with Homer, Lenny is standing beside the donut box, who wasn't seen in the shots before and after. (00:12:15)
Continuity mistake: When Bart crashes at the door of the Legitimate Businessman's Social Club, his head is facing the door. You can only see this for several frames. In the next shot, his head is facing the sky. (00:05:25)
Continuity mistake: At the beginning, when the bus is driving to the school, the streetlights outside disappear/reappear between shots. (00:01:30 - 00:02:20)
Audio problem: Where Lurleen sings the line "I tried to kiss him," on the TV show Ya-Hoo!, you can see that her lips aren't moving. (00:20:35)
Continuity mistake: While Homer is sleeping, his head is facing the 'Core temperature' indicater. When he wakes up, he is in a different position. (00:04:25)
Continuity mistake: When Bart finds out that Homer took the police badge out of the cereal box, it changes from brown to pink. The food inside the box also changes to pink. (00:01:10)
Missionary: Impossible - S11-E15
Continuity mistake: This mistake happens twice in the episode. At first, when Homer arrives on the island, he gives the islanders some bibles and says "Knock yourself out." Ack says that they cannot read. Yet later when Homer is revealing the casino, Ack reads "The Lucky Savage-?"
Suggested correction: Homer had been there for a while when the casino had finished construction. He could have taught Ack to read.
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Carl complains that he can't be fired, everybody behind him, Homer and Lenny has disappeared. (00:09:00)
Other mistake: When the wheel falls off Bart's skateboard, in the shot where he curves left sharply, you don't see the school in the background. How could he be at the social club if he just left school? (00:05:20)
Continuity mistake: When Homer laughs at Patty and Selma, for a few frames you can see that the beer can he was holding is gone. It stays beside the phone for the rest of the scene. (00:07:00)
Suggested correction: When Homer is laughing at Patty and Selma he never has the beer can in his hand. He has a drink then the camera cuts to Marge talking about Patty and Selma, Marge then walks out of the shot, and we get a close up of Patty and Selma. The shot then changes to Homer who starts laughing. Enough time to put the can down.
Continuity mistake: There are three mistakes when court is dismissed: 1) the people standing around disappear, 2) the two men with Fat Tony disappear for one shot, and 3) when Bart says that crime doesn't pay, Marge is suddenly standing beside Bart. (00:20:35)
Suggested correction: There are also 3 corrections here. 1) the only people standing near the bench are Lionel Hutz and Seymour Skinner. Seymour is simply out of shot and Hutz is on screen. 2) Legs and Louie don't disappear they remain standing on the steps but due to the camera angle that is now looking across the steps rather than up the steps so they are out of shot. 3) There is a close up of Bart and Fat Tony long enough for Marge to walk over.
Continuity mistake: Bart puts his lucky red hat on the hat holder. It disappears in the next shot. (00:07:10)
Character mistake: When Homer discovers that the Leftorium is going out of business, there is a sign that says 'Coming Soon: Gum for Less' beside the store. Later on, though, Ned says the new store is becoming 'Libertarian Party Headquarters.' (00:15:50 - 00:19:15)
Suggested correction: The sign is just an advertising poster that's on a wall. It's not in front of the leftorium.
Marge vs. the Monorail - S4-E12
Audio problem: When goes to the Monorail Café, the woman there says to Marge "Go away" but her mouth doesn't move.
Continuity mistake: When Moe tries the Flaming Homer, there are bottles that keep appearing, and the knife disappears suddenly. (00:06:55)
Other mistake: When Bart sees that Santa's Little Helper ate his homework, and the camera moves really fast, you can see that the Krusty Doll and picture frame have vanished from the desk beside his bed. (00:00:55 - 00:01:50)
Dude, Where's My Ranch? - S14-E18
Plot hole: Lisa says Luke was her 1st crush. What about Nelson, Corey, Mr. Bergstrom, Thelonius and the boy that works at the library in 'Bart's Girlfriend'?
Suggested correction: She didn't have much of a crush on Mr Bergstrom, she mainly admired him because he was kind. However you are correct about the others.