Mike Judge actually got the "is this a god dam" joke from his grandmother, and when she told him it, he didn't find it funny at all. Ironically, numerous viewers have since told Judge it's their favorite part of the movie.
In the desert scene, where Beavis and Butthead hallucinate, voices are heard in the background. When the soundtrack is played backwards, Beavis and Butthead are heard speaking clearly, including phrases such as "Everybody go to college, study hard, study hard."
The name David Letterman chose as his credit for his voice-work in the film, Earl Hofert, is actually the name of his uncle, the same "Uncle Earl" Letterman routinely mocks on his show, especially for an incident where a drunk Uncle Earl supposedly said "Here, kitty kitty kitty" to the Thanksgiving turkey.
There's a line in the script that indicates that if 'Bill Clinton' lost his re-election campaign in 1996, there would be a change to the scene where Butt-head meets Chelsea Clinton. In the regular movie, she's folding clothes. But the scene was written so she could also be packing a suitcase instead with only a minor addition to the scene.
The version of "Walk on Water" on the official soundtrack is not the version that is heard in the movie. The version you hear in the movie is actually the 'demo' version, and it appears on Disc 2 of Ozzy Osbourne's 'Prince of Darkness' boxed set.