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.
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.
Continuity mistake: When Beavis & Butthead are walking off with the school's AV equipment, when they get to the outside steps, you can see that they are not dragging any equipment behind them, when they were doing that just a couple seconds before. Oh, and the equipment they were dragging with them does show up after the whole unit falls down the outside steps.