Continuity mistake: There are three mistakes when court is dismissed: 1) the people standing around disappear, 2) the two men with Fat Tony disappear for one shot, and 3) when Bart says that crime doesn't pay, Marge is suddenly standing beside Bart.
Continuity mistake: When Bart crashes at the door of the Legitimate Businessman's Social Club, his head is facing the door. You can only see this for several frames. In the next shot, his head is facing the sky.
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?
Continuity mistake: When Bart realizes he forgot his permission slip, the camera shows us that the paper is half-under his pillow. However, when he got out of his bed at the very beginning, the paper wasn't under his pillow.
Other mistake: When Bart sees that Santa's Little Helper ate his homework, and the camera moves really fast, you can see that the Krusty Doll and picture frame have vanished from the desk beside his bed.