$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Revealing mistake: At the dinner table Homer says something like "as you know it's always been my lifelong ambition to be a blackjack dealer." During this line, for some reason they appear to have used a clip from an older episode (Season 3 / Episode 3 - When Flanders Failed) and dubbed the line over. For one thing, the animation is of a much lower standard than the rest of the episode. And perhaps even more telling, when he says it, he is holding a fork with some food on it, but from the earlier shots we know there is no food in front of him.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.