Continuity mistake: In the scene where the dog chases Snake into a playground, Santa's little helper starts pulling the ropes off the top of the climbing frame, in one shot the dog has two ropes left but when we see Snake the dog chews through one rope and the whole thing falls.
Continuity mistake: After the boy's car gets crushed, Bart sells Milhouse's glasses for $600. Then Milhouse knocks over the Coke bottles and the clerk gets the money back and keeps the glasses. The next scene, where they try to get on a train that goes to Springfield, you can see Milhouse in his glasses and throughout the rest of the episode.
Continuity mistake: In the scene where the FBI agent and Homer are going into the photo booth to view the video, look to the right of the photo booth before they enter. There is a white cup next to the booth. After they have watched the video and are standing outside the booth talking, the cup is now red instead of white.
Continuity mistake: When Bart and Ralph twist the key into the armed switch, the armed sticker is red and the off sticker is yellow. Then, during the press conference, the stickers switch colors. Then, when Mayor Quimby sits in the electric chair, they switch back.
Continuity mistake: In the new opening sequence (season 20), you see Kearney and Jimbo sawing off the Jebediah Springfield statue's head, which starts falling down. In this wide plan, overhead and closing up, the whole town square is in full sight with no one visible besides those characters. The shot cuts to a close-up of the statue's head falling on Ralph Wiggum, now right next to the statue's pedestal where he was calmly eating an ice cream cone.
Continuity mistake: When the dentist shows Ralph the Big Book of British Smiles, he first shows him a picture of Sherlock Holmes with horrid teeth and all of his teeth are there. When Ralph starts getting terrified of it, it shows the same picture, but this time one of his teeth on the bottom right hand corner of his mouth is missing.
Continuity mistake: Immediately after being chained to a tree, Stampy crushes several objects (a lawnmower, a bike, a doghouse, and a trash can). In the very next shot, which comes after a commercial break, all of these objects are in fine shape. Then the shot changes again and we see them destroyed once again.
Continuity mistake: When the women of the neighbourhood throw Marge a baby shower because she's pregnant with Maggie, Ruth Powers is one of the ladies there. Ruth only met Marge when she moved to Springfield with her daughter in "New Kid on the Block" (Maggie was already born in the episode).