Continuity mistake: When the family are watching Krusty Komedy Klassics, at the beginning of the show, they all have grey tables, with their dinner. But when Bart asks for milk, Marge gets up to get it and her table has disappeared. When she comes back the table has re-appeared.
Character mistake: Moe says that no women have been to his bar since 1979, yet in "Flaming Moe's" he hires a female waitress. Also, in the episodes "New Kid on the Block" and "Homer the Vigilante," Ruth Powers appears in the bar, and orders a beer in the former episode while Marge visited the bar in "Bart Gets Hit by a Car."
Continuity mistake: When Homer is starting to go crazy and Ned's face has all the eyes, you can see Jasper in a blue tent. Homer runs away from Ned, going past Jasper's tent, up to a crowd of people...which includes Jasper.Dan23
Continuity mistake: When Grampa Simpson says "That's the activity room" to Mr Burns at the Retirement Home, you can see that Mr Burns and Grampa both have glasses on their trays. In the next shot, Mr Burns' glass is on the table and Grampa's glass has moved from the left to the right.