Continuity mistake: When Burns is lay on the floor telling Smithers that he dreamed of Marge again last night, the painting behind Smithers is very badly painted and very childish in appearance. Burns' head is completely disproportionate for example. When the shot changes to Smithers the painting is now a lot more detailed and no longer looks childish. (00:14:42)
Revealing mistake: When Homer points at the donut guy, his right shirt cuff is colored yellow. (00:12:50)
Other mistake: When Homer pretends to read the newspaper, the back page is very noticeably blank and missing any print. (00:08:00)
Continuity mistake: During the musical number about Mr. Burns, Homer and Marge swap sides of the table. (00:05:40)
Revealing mistake: At the start when we see stuff falling off the roof, the animation for the swings in the background simply fade out and are incomplete. (00:02:05)
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.