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. (00:05:25)Yoshi
Continuity mistake: This mistake happens twice in the episode. At first, when Homer arrives on the island, he gives the islanders some bibles and says "Knock yourself out." Ack says that they cannot read. Yet later when Homer is revealing the casino, Ack reads "The Lucky Savage-?"
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? (00:05:20)Yoshi
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. (00:20:35)Yoshi
Character mistake: When Homer discovers that the Leftorium is going out of business, there is a sign that says 'Coming Soon: Gum for Less' beside the store. Later on, though, Ned says the new store is becoming 'Libertarian Party Headquarters.' (00:15:50 - 00:19:15)Yoshi
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. (00:00:55 - 00:01:50)Yoshi