Plot hole: In the last part of the episode, when Mr Burns is trying to convince Homer on his float to play a big prank, the timing is totally wrong. Firstly, Lisa sees the writing 'Happy Pranksgiving' on the side of Mr Burns' float way before it reaches her, and it takes Mr Burns ages to change into the Father Christmas outfit.
Continuity mistake: When Homer, Lenny and Carl are in the cafeteria, and Homer is drinking beer, his chair changes from being blue, to red, then back to blue again, between different shots. (00:06:45 - 00:07:15)
Deliberate mistake: The mouth on the panda costume is in a constant smile and at no point does Homer change it, even when he is in pain. However, when he is being pulled back under the curtain the mouth is open and the mask has a frightened expression. I suppose this was done on purpose, but it's still a continuity error of sorts.
Continuity mistake: When the Simpsons are at the restaurant at the start, Bart has no medal on his jacket. But when Lisa remarks a few seconds later that Homer gave Bart a medal, one has appeared on his jacket.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.