Continuity mistake: After the safety expedition has taken place, we see that when everyone is in Burns' office that by his main doors there are 4 buttons on the wall. Yet when a shot from further away is shown, they are not there.
Continuity mistake: During the song "Its the American Way" Snake is robbing Hans Moleman during Chief Wiggum singing and Snake's hair is blue. His hair has always been a brown-red color. In the very next scene to confirm its a mistake you see him in the park saying "Yo Sherry Bobbins" and his hair is back to its brown-red color.
Continuity mistake: When the flashback of Ned and Todd Flanders singing in the Simpsons' doorway, Homer says he could use a TV tray. Then it goes back to the present time and Homer picks up a beer from the TV tray which is next to the couch. The TV tray was never there at any other point in the show. (00:10:40)