Revealing mistake: At the dinner table Homer says something like "as you know it's always been my lifelong ambition to be a blackjack dealer." During this line, for some reason they appear to have used a clip from an older episode (Season 3 / Episode 3 - When Flanders Failed) and dubbed the line over. For one thing, the animation is of a much lower standard than the rest of the episode. And perhaps even more telling, when he says it, he is holding a fork with some food on it, but from the earlier shots we know there is no food in front of him.David Mercier
Deliberate mistake: When Bart is in the genius school, the teacher asks him if he knows what happens if he adds an acid to a base. He replies yes, adds them anyway and the lab explodes and a green goo comes out, turning Bart green. If you add an acid to a base, you just get salt and water.SexyIrishLeprechaun
Continuity mistake: The guardrail at the Springfield Gorge keeps changing between shots when Bart is about to make his big jump; in the first wide shot there is a short rail opposite the "stone ramp." Then in the Bart-POV shot from atop the ramp, the rail is much longer, and the parking lot and picnic area behind it have disappeared. And when Homer is actually jumping the gorge, the rail disappears altogether.
Continuity mistake: In the end of the episode when the family has reclaimed the house and are cleaning up the living room. As Homer mentions about letting the Cooders stay, Bart tells Marge to get him away from the window. She is standing right next to the couch in the lounge but the very next shot she lowers her hands and pats the couch yet is now in the family room. (Note: There was a few shots that showed there was two couches so the mistake is with Marge suddenly moving not the couch.).Lummie