Factual error: When you see Ned Flanders put the earth back inside the hole, he puts it back in much faster than is possible. In one shot, he is only just starting to put it back in, then you see Bart who talks to himself for a few seconds, then back to Flanders, who has finished burying what is later to be revealed as the plant that he (Ned) drowned.
Continuity mistake: In the scene where Lisa runs into the attic as she dives behind the chest she rattles a bird cage, later when Ned faints you can see that the bird cage has disappeared.
Revealing mistake: When Bart is watching Rod and Todd walk over to Ned Flanders, you can see their reflections on Bart's telescope. Their reflections do not match their actual positions.
Other mistake: When Bart is looking at space through his telescope, Earth can be seen through the telescope despite him being on Earth.
Other mistake: When Bart is looking at Doctor Hibbert on the rowing machine, all the pictures on the walls behind him don't have faces on them.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.