Factual error: After Bart's prank call with Moe, you can see Bart and Lisa laughing. However the telephone's wire does not connect to the receiver. (00:09:40)
Revealing mistake: During the first ten minutes when the twins are explaining to Bart what incompetence means, one of the twins' body disappears, showing a floating head and hair. (00:06:30)
Continuity mistake: In the park, Marge's necklace changes from white to red. (00:15:40)
Continuity mistake: When Sherri and Terri raise their hands and say "like us Mrs. Krabbapple" they raise their hands over their heads. Camera cuts and their hands are a lot lower. (00:04:20)
Continuity mistake: On the bus at the start there are some lines on Mrs. Krabbapple's microphone. They disappear when she tells Bart to sit down. (00:03:00)
Continuity mistake: At the very start the twins are stood facing each other. Camera cuts to behind and now they are side by side. (00:01:20)
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.