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.
Continuity mistake: When Marge and Homer are at the Springfield formal ball at the Country Club, about half way through the ball, there is a woman with her back to the camera as she is talking to Marge and Homer. Homer is on Marge's left side. In the next shot when Marge's back is to the camera and you can see Marge still talking to the woman, Homer is no longer on Marge's left side, he is gone.
Continuity mistake: When Bart is in the ice cream parlor breaking up with Greta, the waiter tells him "We get that a lot around here" and point over to Chief Wiggum and Lou sitting behind and to the left of Bart. Bart turns his head all the way to the side to see them. The focus then goes to Chief Wiggum and Lou, but when their part is done and the "camera" goes back to Bart and Greta, the policemen are sitting behind and to the right of Greta, so that Bart would not have had to turn his head to see them.
Continuity mistake: After Homer's father, Abraham, comes home after a night out with Zelda, Homer snatches his keys away from them. He leaves his hand out and begins outstretching fingers one by one to represent all the people he called in worry, and it's clear that the keys have disappeared.
Continuity mistake: In the cinema, it is clear that the people attending the movie keep on changing. For example, For a few shots, you can see that Krabappel and Skinner are sitting in the front row, but the next time you see those seats, they have been replaced by Lenny and Carl and Krabappel and Skinner aren't in sight.