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.
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.
Continuity mistake: When the hamster Nibbles has rolled back to Skinner, it takes the lid of the ball off, and the lid lands on the ground. When the hamster is rolling away from Skinner it doesn't put the lid back on, it just leaves it on the ground, but in the next shot the lid is suddenly gone.
Other mistake: Apu already knew Homer because in the flashback episode, Homer's barbershop quartet, they were in a band. However, in the scene where Homer enters the Quick-E-Mart, Apu refers to Homer as steady customer as if he didn't know him.