As was listed in another goof, there were some inconsistencies with the scores during the Greek Games portion of the Homecoming Carnival. Part of this is because one of the events, a Chariot Race, was cut from the final version of the movie (the Chariot Race can be seen on the "panty raid edition" DVD under Deleted Scenes.)
When the horn players begin to play, officially commencing the Triathalon, the trumpet player on the right does not lip synch on cue. Towards the end, he is taking breaths when instead, he should be blowing into the instrument.
In most frames of the Homecoming Carnival skit performed by the Pis, they clearly aren't singing, yet multiple voices are heard singing throughout the song. At one point in, the girls grunt at the same time they are singing.
In the computer lab, when Judy and Gilbert first meet (visible in the distant "behind the computer" shot at the beginning of the scene). Possibly only visible in open matte fullscreen versions of the movie.
During the Lambda/Omega Mu song, when Lamar is singing, Poindexter can be seen "bumping" to the music (going up on their toes) out of time with the others. Possibly deliberate since he is shown to be uncoordinated throughout the film.
When Gilbert begins making his "I'm a nerd" speech near the end the film, his jacket sleeve is stained with dirt from the Alpha Beta attack just moments ago. During the speech, the dirt appears and disappears between shots.
During the Greek Carnivale competition, The Alpha Betas are leading the Tri-Lambda team 30-20 going into the belching competition. Even though the Tri-Lambs win that competition, the Alpha-Beta's overall lead increases to 40-25.
Following the belching contest, the score board shows the Alpha Betas with 40 points, and the Lambdas with 25. In the background of the first javelin throw in the next scene, the score board shows the Alpha Betas with 25 points, and the Lambdas with 10 points.
When Coach Harris lectures the jocks following losing at the homecoming carnival, behind him is a blue wall with text reading "Only the strong shall survive" and a door that reads "COACH HARRIS." But when the Alpha Betas run out of the locker room, the blue wall has become white and there is no writing on it.
At the Pep Rally, when UN Jefferson shows up and the coach lets go of Gilbert and the mic stand, Gilbert stumbles out of frame away from the stage. When UN Jefferson goes to hand Gilbert the microphone, he is laying on the ground right in front of the stage, next to to the mic stand.
The trichloromethylene Takashi takes to counteract the alcohol does not exist. A common misconception is that they are talking about chloroform, which is also known as trichloromethane. Ingesting chloroform would have very different effects.