In Viva Ned Flanders, the direct prequel to this episode, we see the wedding video, which shows Amber and Ginger kissing their respective husbands forcefully. However, when the video appears here, Homer and Ned drunkenly kiss each other.
Judge Harm claims bigamy is legal in Nevada. However, it has been illegal there since 1911.
Not only is bigamy illegal in Nevada, isn't legal anywhere in the United States.
When the Simpsons are playing Monopoly, Bart had several houses and hotels on Marvin Gardens. In the rules of Monopoly you're only allowed up to 4 houses or 1 hotel in each property.
Acid rain, while destructive over time, is nowhere near as concentrated as portrayed in the episode.