Continuity mistake: The right handle plate on Homer's gun is fastened with two screws throughout the entire episode. But in the scene where he promises Marge to get rid of the gun and they hug in the kitchen, the gun is seen lying on the table with only one screw in the handle.
Continuity mistake: When the Home security seller is first seen, he steals an ashtray and a remote control off a speaker and turntable player both close to each other, When the shot changes the speaker and turntable player are much further away from each other.
Continuity mistake: At one point Marge says "no guns at the dinner table" and Homer says "you said the breakfast table", then Marge replies "it's the same table". In most episodes they eat dinner at a different table.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.