Other mistake: While Homer is in Lisa's bedroom trying to make things right with her, there are three pictures taped to Lisa's mirror. After Homer tells her the music may help, in the next shot Homer walks over to stand behind Lisa. Those pictures taped to Lisa's mirror are weirdly behind Homer's reflection, as if the pictures are taped to the wall behind Homer. Three shots later, when Homer tells Lisa he can fix the dollhouse, his reflection is accurate in relation to those three pictures taped to the mirror. (00:19:20)
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.