Revealing mistake: When Lisa hugs Homer, there's a person next to her with a missing head. (00:21:43)
Continuity mistake: When Homer has the Bill Of Rights, he ends up ripping several parts of it. The rips keep alternating between shots. (00:05:25)
Other mistake: When Marge takes Homer back inside, his car is seen blocking the traffic. But at least one side of the traffic is driving on the wrong side of the road. The drivers behind Homer's car are on the right side of the road. And the drivers behind Homer's car from the opposite direction are driving on the left side but facing the drivers behind Homer's car on the other side. Either way, one half of the traffic are driving on the wrong side of the road. (00:02:35)
Other mistake: When Homer returns home, Marge says his car is blocking the traffic. But there is some space on the road where his car isn't. The traffic could easily have driven through the empty space. (00:02:30)
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.