Other mistake: In the beginning of the episode when Chief Wiggum orders a battering ram through the front door of a house, Reverend Lovejoy opens the door and questions what they are doing. Chief Wiggum says "isn't this 742 Evergreen Terrace?" to which Lovejoy replies that it's the house next door. In the next shot, you see Snake pulling out of the garage and speeding away. Everybody knows that 742 Evergreen Terrace is, in fact, the Simpson residence.
Continuity mistake: After the aliens have dropped off the Simpsons in their back yard, Marge is seen wearing her usual red pearls. Except in the final shot of the family. Then her pearls are white. This is not due to the alien light source altering the colors in the segment, because Marge's pearls have been a dark color through the whole episode, even inside the alien spaceship.
Continuity mistake: When the children are sleeping in the canteen at school, Bart is resting his head on a red sweater. In the close up of him and Lisa, the sweater has now turned dark green. It's not because of the dark that we see it like that because there is a bit of light at the beginning of the next shot and we see the jumper to be dark green.
Factual error: When Bart declares war on Nelson, Herman uses the declaration from the Franco-Prussian war and puts "Bart" in place of "Otto Von Bismarck". The thing is, Bismarck didn't declare the Franco-Prussian War, Napoleon III of France did. A small error, maybe, but something that a war buff like Herman should know.
Other mistake: Bart and Lisa overload the nuclear power plant to create a city-wide blackout so everyone can see the meteor shower. All the lights in Springfield blow out. Yet when we see the Simpsons sitting on their lawn watching the shower, every single window in their house is yellow, as if every room has their lights on. It is the only house shown with power.