This is the first time we see Inspector Spacetime. This is a parody of Doctor Who (1963) and is shown throughout the series.
At the beginning, the Dean says, "This is the kind of National Lampoonery that is coming to an end this year!" This is an allusion to Chevy Chase who is widely known for starring in the movie Vacation (1983), and its many sequels/spin-offs.
Jeff's appearance, following the gassing in the vents, is a reference to Jack Torrance in The Shining. The denim shirt, the powder resembles the frost, and he is wielding an axe.
Pierce attended the Laser Lotus Celebrity Center, a reference to the Scientology Celebrity Centers.