Revealing mistake: When Skinner talks to Otto on the bus, the point of his hair is touching a pole. Look at the pole - Skinner's hair is going through it.
Revealing mistake: At the U.N. meeting, Bart places his glasses down on the table to read out the Libyan exports. As he puts the glasses down, you can see they are unrealistically floating in the air.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.