Continuity mistake: When Homer gets mad when Carl calls him "Chrome Dome", there is a fish stick on his plate, but in the next shot, the fish stick has disappeared.
Continuity mistake: When Homer is speaking to Carl and Lenny at the coffee stand, there is initially nothing in Lenny's cup, but a few shots later his cup is now full without him filling it.
Continuity mistake: When Homer is rolling around on the grass outside the house with Bart, Lisa, Santa's Little Helper and Snowball II after the hair formula works, Snowball II is drastically larger than usual in the overhead shot.
Continuity mistake: When Homer and Karl are selecting a suit, just after Karl says none of the suits are to his liking, Karl's tie changes from green to red.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.