Continuity mistake: When Homer sees the hotdog that Duffman holds up near the end of the episode, the order of the condiments on the hotdog change in subsequent shots.
Continuity mistake: Before Homer sees his vision of Caesar Romero the day sign next to him says 9. After the Duff executives see him talking to nobody they decide to take him away and when they get down there the sign now says 12 with the president of Duff confirming it in his speech. Doubtful it took them 3 days to get down to him and not much reason for Homer to take 3 days off the sign seeing as he was almost passing out from the lack of food.
Continuity mistake: When Homer is eating the sausage, a square on his shirt disappears in a shot from his feet and then is back in the next shot.
Other mistake: When Lisa says Bart's got a girlfriend, Bart says "no, I don't, that's the problem", his neck becomes longer and starts to wobble, a problem with the animation.
Continuity mistake: Lenny's mug refills itself when he tells Homer, "You want to help me?"
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.