Continuity mistake: When Homer is stuck in the hole after saving the plant, Marge is seen in the background wearing lipstick. When Mr. Burns asks if there is anything he can do for them, there is a closeup of Marge and her lipstick is gone. When they cut back to Homer, Marge is again wearing lipstick.
Factual error: If Homer's stomach was really caught on the towel rail the way they show it to be, he wouldn't be able to see the scales at all without having to look round it.
Continuity mistake: When Homer says he's going to the cinema, we see his drinking bird working in front of the computer. It makes a key press on the lower right of the keyboard, however on the following close up shot of the bird pressing the Y key it is a standard qwerty keyboard layout.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.