Continuity mistake: Season 20, episode 16, "Eeny Teeny Maya Mo." In the scene where Moe is cleaning his window inside the bar, take notice that the size of the spot he cleans on the inside of the bar is small. But when the shot changes to the outside, with Moe and the others looking out from the inside, the clean spot is larger.
Continuity mistake: Season 20, episode 16, "Eeny Teeny Maya Mo." As Marge is feeding Maggie a grapefruit, Bart takes out his bongo drums and plays them. Watch as Bart plays - the shot zooms in from the back of Bart towards Maggie, and you can't see Marge in the scene sitting close to Maggie; the next shot shows her though.
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.