Continuity mistake: When Hans Moleman and Rev. Lovejoy are in the prison they are sitting to the far right of the bench (which is nearest to Homer's cell). Then in the next shot they are to the far left.
Continuity mistake: When Homer calls the Fatherhood Institute about his poor test results, the guy is holding a cup with 'Super Dad' on it. In the next three shots the cup has jumped to being on his desk.
Other mistake: When the wheel falls off Bart's skateboard, in the shot where he curves left sharply, you don't see the school in the background. How could he be at the social club if he just left school?