Continuity mistake: When Bart is first introduced to the Superfriends, Ham moves around the table a bit. First he is seen sitting next to the kid with dark, curly hair, and you can see a plate in between him and Bart's plate, indicating that someone else is sitting there. This someone turns out to be Lisa, who after she is introduced, switches seats with Ham, making Ham sit next to Bart.
Continuity mistake: When Homer is walking upstairs after kicking Patty and Selma out for the second time, the wall that Homer was approaching is a darker colour than it usually is, and Homer walked up the stairs slowly. But a second later he closed a door, indicating that he went into a room. Are we really to believe that he could go very quickly from the stairs to a room in a matter of seconds?
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: During the big song near the end, there is a birds eye view of everybody outside dancing and singing, and Krusty, Chief Wiggum and Skinner are there outside with everyone. But in the very next shot, they all appear out one of the windows, singing a line to the song.
Continuity mistake: When Marge is typing her novel on the computer, in one close-up shot of her we see there is a pencil on one side of the table and a pot of flowers on the other. Yet when the shot changes to further away we can see that the pencil has been replaced by a napki, a pot with two pencils has appeared, and the flowers have moved to this side of the table as well.
Continuity mistake: When Lisa first discovers Jebadiah's confession, she is holding the fyffe and wearing his racoon hat, the screen fades to black (I'm guessing for the ad break) but when it comes back Lisa is standing in exactly the same position, still reading the confession, still holding the fyffe, but no longer wearing the hat.
Continuity mistake: There are two problems with Lisa's Indian burns. When we first see them, she has 4 burns. Then, while she is showing them to the bullies, there are 3, then 4 again. Then, in the very next scene when she is walking with Nelson in the schoolyard, they are gone altogether.