Continuity mistake: When Chief Wiggum and Homer think that the convertible Ruth and Marge are in is a ghost car, they want to hold each other. In this shot, you can see 1 small star out of the backseat of the police car. But in the next shot, from the perspective of the backseat, there is a canyon top where the star would be.
Continuity mistake: When the Simpsons first see Artie Ziff in the attic, as he stands up, there's a theremin behind him (corresponding with Homer's comment that the "ghost" was playing his theremin). Artie puts a sign up above it. However, when Artie moves to the rafters, the sign he put up is still there, but the theremin isn't.