Continuity mistake: When wedding has been just called off, Lunch Lady Doris calls everyone for wedding cake, and among people who rush to it we can see Moe (you can recognize him by his eyepatch), then, Lisa starts to walk off and among the people she passes by you can see both Lunch Lady Doris and Moe.
Continuity mistake: By the vending machine, Lisa first points her card at the cell on the right, then there's a zoom on the cells and we see her hand starting to point again, but this time at the cell in the middle. In the next shot, she lowers her hand with the card, which however in this shot is pointing at the cell on the right again.
Continuity mistake: When we first see union flag on fire, the flames are already consuming over the half of its upper edge. Then when we see it reflected in Hugh's eyes, no more than a half of the edge is burning.
Continuity mistake: When Lisa enters the taxi and we see the door being closed, the camera turns into the full view of the taxi in the next shot, and now we see that the door (the one with company logo on it) has changed its shape between shots.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.