Tree House of Horror VIII - S9-E4
Other mistake: In 'Homega man', Homer goes into the bomb shelter and does not shut the door, and you can still see it open for a while after he is in there. Herman does not close it behind him - you can tell by his skeleton's position. But Homer opens the door to leave the shelter after he has eaten the food, and it must have been closed for him to have survived the atomic attack, because it vaporised Herman, who was only a few feet away.
Other mistake: When Homer is muttering whilst walking up and down the home landing at night after being told he has to wait 5 days to receive his gun/license, Lisa being awoken by his muttering complains that it is 3am but her bedside clock shows 9.50/21.50. (00:06:55)
Other mistake: When everyone is eating the boar at the end, the boar is completely intact, yet everyone except for Lisa is seen with a piece of it. (00:20:30)
Other mistake: When Bart, Lisa and Milhouse run away from the others, Lisa steps right on a puddle but no splash or ripple is made.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.