Right before question #6 of the oral make-up exam, there is a brief shot of the basketball game, and the score shows 32-32 with 50 seconds on the clock. Yet, prior to that, the half ended with the score 41-33.
When the basketball player emerges from the locker room shower, he is carrying his towel in front of him. In the next shot, the closeup, the towel is draped over his right shoulder.
That the flag in the Custer College gymnasium has 48 stars is not necessarily a Goof. Although the movie was filmed in August 1959 and the 48-star flag became outdated in January 1959 when Alaska became a state (and the 49-star flag likewise in August that year with the addition of Hawaii), 48-star flags were still in widespread use. This would be especially true at private institutions (such as Occidental College, whose gym was used for filming), where the year's budgets already had been set.
In the several instances where the bribery money is shown, it has the appearance of real money, mostly $50 and $100 bills, but when Fred Jensen (Tom Laughlin) is counting it in the final sequence, it is obviously stage money.