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: The location of the comet in the sky changes direction at several points. Whilst it's apparent size and altitude will of course change, the direction it is coming from cannot. As an example, it is seen looming over the power plant towers, but when Ned is on the hill, it's no longer there.
Revealing mistake: In the scene where the family is in the car, driving home from The Town hall meeting, Homer says "the whole reason we have elected officials is so we don't have to think all the time!" When he says "don't" a second collar appears beneath the right collar of his shirt, and then disappears after he says "time." (00:11:20)