Revealing mistake: When Lisa is clapping erasers, you can see the alphabet above the board, and part of the A is cut off.
Continuity mistake: After Bart finds out that Lisa took the teacher's books, his Hall Monitor sash disappears and reappears for several shots. (00:20:05)
Continuity mistake: When Bart uncovers the photo of the Simpsons behind the books in Lisa's locker, the books change between shots.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.