Continuity mistake: When they are in the Whitehouse, and Beavis has turned into Cornholio, he picks up the "Red" hotline phone on the President's desk, and is talking to the nuclear bomb officials. Later, when they are in the President's office again, getting their certificates, there is now a black phone on the desk, where the red one was.
Plot hole: When Butthead pushes Beavis out of Muddy's car, Beavis causes a huge car crash. Then, a few seconds later Butthead falls out and causes cars behind him to crash, but the crash that Beavis started made a barrier along the highway, so how could those cars get behind Butthead so fast?
Continuity mistake: As Beavis and Butt-head are dancing in the casino the floor is just flat and one surface. In the overhead shot of them dancing you can see part of the floor has changed to an tiled area instead of a plain flat surface. Also there are a number of people sitting at tables just in front of them whilst dancing. In the overhead shot they and the tables have disappeared.