Continuity mistake: When Moe is going to get a plastic surgery, the surgeon draws some marks on his face. You see Moe from a side view, and the marks on his face aren't visible from that angle. However, the marks on his face suddenly appear and you can now see them from that angle.
Continuity mistake: When Lisa is on the television talking about her tax rise, we see inside Moe's tavern. Look at where Lenny and Carl are sitting because they have moved 3 or 4 seats down when we go back to them later on. And there is no reason why they would they move like that.
Continuity mistake: When the Ranger stops the Simpsons' car at the start of the episode, watch his "class ring". When he puts his hands inside the car it's on the left hand. However, the flies later eat his hand and take his ring, and it's suddenly his right hand they ate and took it from.