Continuity mistake: When Bart and Lisa are trying to win back Homer's affection they are sitting on the top of the stairs and push the skateboard with the present on it down the stairs. In the next shot it rolls into Homer's legs yet it would be impossible as he was standing in the main living room which is to the right of the stairs. Pushing the present down the stairs it would go straight into The Front door.
Continuity mistake: When Bart is standing on the bench, Jimbo and Milhouse are standing in The Front row, on the right side of the screen. But when there's the closeup (a second later), there are children shown in front of Jimbo and Milhouse and the girl with the purple hair is gone.
Continuity mistake: In "Wiz Kids", Bart stabs Montymort in his shin which is open (i.e. not covered by what he's wearing). Only a little blood pours out. Then Monty raises his shin into shot and there is not only a puncture in the leg of his clothing, but the wound is covered in blood. When he falls, and Slithers eats him moments later, there is no damage at all. (00:19:55)
Factual error: When you see Ned Flanders put the earth back inside the hole, he puts it back in much faster than is possible. In one shot, he is only just starting to put it back in, then you see Bart who talks to himself for a few seconds, then back to Flanders, who has finished burying what is later to be revealed as the plant that he (Ned) drowned.