Continuity mistake: When "The Leader's" car drives by, trailing a cloud of dust, the dust doesn't appear on the people's robes until the cloud clears away.
Continuity mistake: When Homer is fishing, the colours of the things on his hat switch places between shots.
Continuity mistake: When Frink collapses at the table, his sleeves are green. When it cuts to a wide shot, they are yellow.
Continuity mistake: When Bart and Lisa are in the compound, just before Bart gets brainwashed, the bags that were behind Lisa disappear. Homer and Marge were on the other side of the room, so they couldn't have picked them up.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.