Continuity mistake: When Moe picks up the "Malaysian Beer" and says they don't serve Duff anymore and how good it is, you then see a shot of Homer talking, then when Moe has put down the beer, it's a Duff .
Much Apu About Nothing - S7-E23
Plot hole: At the end Apu finds out he's been chosen for jury duty for the first time. However, in 'The Boy Who Knew Too Much' he was on the jury.
Continuity mistake: In the initial robbery at the Kwik-E-Mart, Apu doesn't realise what's going on until the fake Krusty demands the money from him. Yet in the video shown in court, he turns to face the fake Krusty right as Homer screams.
Continuity mistake: Lisa places her Gaspacho on the house end of the table but in a following shot it's at the other end when the dog is drinking it.
Continuity mistake: When Homer is at Moe's tavern talking about Marge, the level in his beer glass keeps changing even if he doesn't drink.
Marge Simpson in 'Screaming Yellow Honkers' - S10-E15
Deliberate mistake: When Marge goes offroading to get home there is a grassy field which leads right up into the Simpson driveway. However, in all other episodes there is no grassy field and instead there is a house in the spot where the field would be.
Continuity mistake: When the person delivers the animation cell, his skin changes from white, to brown and then back to white. When Bart looks through the letterbox to see who was there, his skin is white. When he gives the box to Bart, it is brown. When he hits Bart in the face and says "that's for keeping me waiting", it is white again.
Burns Verkaufen der Kraftwerk - S3-E11
Audio problem: When the drunks find out they're going to Hawaii, one of them says "Maybe I'll marry Elizabeth Taylor." If you look at their mouths, though, they don't move right. (00:09:50)
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)
Continuity mistake: In the beginning, when Bart finds that the dog ate his homework, the poster on Bart's door has disappeared for one shot. (00:01:45)
Continuity mistake: When the mobsters enter Skinner's office, the phone on his desk changes position between shots. Also, the name bar on his desk doesn't read anything on it. (00:13:50)
Three Men and a Comic Book - S2-E21
Continuity mistake: When Bart, Martin and Milhouse start to fight, the Radioactiveman issue 1 that they were protecting has disappeared from the table. Then when Marge brings up some food, they all start eating. The table has disappeared altogether.
Revealing mistake: In the shot of Skinner admiring his tater tots, he is interrupted and lifts up his tray. As he inspects he tilts his tray to at least a 90 degree angle but everything, including the milk, stays in exactly the same spots.
Factual error: When Rod and Todd Flanders are roasting marshmallows in the car, Todd's marshmallow was the only one above the lighter, even though both of them have turned black. (00:17:40)
Continuity mistake: John is wearing Homer's old "Pin-pals" bowling shirt when the Simpsons first meet him, but only after we see the back of the shirt does the name "Homer" appear over John's breast-pocket; clearly there was nothing there during their entire previous conversation. And even if this is a deliberate "mistake" for comic purposes, in 7th season episode"Team Homer", the very same bowling shirt is ripped to shreds when Homer is being mauled by Mr.Burns' dogs at the very end.
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: When Homer and Marge are discussing about unhooking cable, the time on the clock on Homer's bedside table changes between shots.
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: When all the kids are watching TV, we see Wendell, Martin and Milhouse. Absurdly they appear to be right below the ceiling in this shot - when in every other shot they are sitting on the sofa or standing.
Burns Verkaufen der Kraftwerk - S3-E11
Audio problem: When Horst is checking the power plant, he sees some radioactive liquid pouring out of the chimney, he says "That shouldn't be" but his mouth doesn't move when he says "be". When he spots the raccoons he speaks but his mouth does not move at all. And at the end when Mr Burns is mocking the German men, Horst says "Burns, stop it." but his mouth doesn't move. (00:15:30)
The Last Temptation of Homer - S5-E9
Continuity mistake: When Homer and Barney are at Moe's, Barney drinks his beer and then his cup his empty, and Homer's is full. Then later, Homer's cup is empty and Barney's cup has magically refilled itself.