Continuity mistake: When Lisa first discovers Jebadiah's confession, she is holding the fyffe and wearing his racoon hat, the screen fades to black (I'm guessing for the ad break) but when it comes back Lisa is standing in exactly the same position, still reading the confession, still holding the fyffe, but no longer wearing the hat.
Continuity mistake: There are two problems with Lisa's Indian burns. When we first see them, she has 4 burns. Then, while she is showing them to the bullies, there are 3, then 4 again. Then, in the very next scene when she is walking with Nelson in the schoolyard, they are gone altogether.
Factual error: Homer creates a giant sugar ball by making a normal sized cotton candy on a paper cone, and then coating it with liquid caramel. The cotton candy holds its shape and Homer continues to expand it with more cotton candy and caramel. However, cotton candy dissolves very quickly and tears apart easily. Between the weight and moisture content of the caramel, the original cotton candy would have immediately melted and/or collapsed.
Audio problem: When Principal Skinner is watching the kids throw the books in the fire, someone goes to throw Huckleberry Finn into the fire. He says "Not Huck Finn. I spent hours crossing out the sass-back." While he says this, his lips don't sync with the words.
Continuity mistake: The vehicle they are driving changes form when they drop off Bart at military school to when they drive home. They leave with Homer's purple car (obvious from the crumpled headlight) and as they leave the military school it's Marge's orange car (obvious from the ski racks and lack of a trunk). It's clear from the entire scene that this is all one trip.
Continuity mistake: When Homer is watching TV early in the episode, he has a watch on his left wrist. When he begins working on filling out his tax forms, the watch has disappeared. When he takes down the sailboat painting from the wall, the watch has returned.
Continuity mistake: When we first see Willie standing by the Black Wall of field trips, the latest entry is at Willie's eye level. But when the angle changes, there are a lot more names on the wall, making the last entry appear just by Willie's chest.
Continuity mistake: The stocks that are put on Marge and Homer are fitted so that their head and hands are secured and cannot be removed. Whilst in Flanders garage and Homer is using the rotary saw to remove Marge's stock, Homer's stock is still secured on him but his arms and shoulders are through the stocks.