Continuity mistake: The lettering on Smithers' desk name plate changes between shots. While he is taking the call from Mr Burns' mother you can see his name "W. Smithers" in black letters. The shot after seeing Burns, who keeps falling asleep, the letters are now red.
Continuity mistake: When Homer gets up to make Mr. Burns' breakfast, Marge's nightgown is yellow, making her look naked, but in the next shot, her gown is purple.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.