Continuity mistake: When Bart and Nelson first roll the orange and apple, we can see there is no-one sitting in front of Nelson. But a couple of shots earlier, we saw Milhouse sitting in front of Nelson.
Continuity mistake: On the bus, Otto rewinds his tape and there is a shot of the kids. In this shot, we can see the kids and nothing else. A couple of shots later, a food box has appeared out of nowhere.
Revealing mistake: At the U.N. meeting, Bart places his glasses down on the table to read out the Libyan exports. As he puts the glasses down, you can see they are unrealistically floating in the air.
Audio problem: When Homer says God is his favourite fictional character, his mouth is saying something different to what we hear.
Audio problem: When Homer is placing objects on the dining room table to start his website, he is whistling but his mouth isn't moving.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.