Continuity mistake: In the scene when Homer is signing up for the naval reserve, the administrator gives him a pencil to fill out his form, but when the camera moves to The Front of Homer it changed to a pen.
Continuity mistake: In the scene at the United Nations, the Russian placard is just a placard. In the next shot, the placard is attached with a rod to rotate it at the push of a button.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.