Continuity mistake: Bart's coat gets covered with dust during the fistfight in the cabin. But in the next shot, he runs outside and the coat is completely clean again. (00:47:00)
The Town That Wasn't There - S4-E3
Continuity mistake: John Astin, playing a homely sheep farmer, wears a large fake nose throughout the episode. But in the saloon meeting scene, where Beau introduces him to the townsfolk, the nose is conspicuously missing.
Continuity mistake: In the opening scene, rear-screen projection footage behind the stagecoach shows a landscape covered with trees. When Crippen points out the mountains, we see an expanse of completely treeless desert. In the next shot, the trees have returned.