When Abed says Jeff is "Goldbluming", referring to actor Jeff Goldblum, Jeff unintentionally impersonates Goldblum. This is a reference to Goldblum's 1986 movie The Fly (1986).
Jeff (plus Annie and Abed) take a pottery class in this episode. In a previous episode, Football, Feminism and You (2009), Troy tells Jeff to "take a pottery class or something".
Jeff notices Rich's license plate is New Mexico and remarks 'long way from home' - while the show takes place in Colorado, the state directly north of New Mexico.
"Throwing off the hump" is indeed a very advanced pottery technique. It means forming a vessel on top of a giant hump of solid clay, so you work just with the top of the hump of clay and cut it off when done. The show depicts this, but got wrong that the professor would be able to see it was thrown off the hump just by looking at it. Jeff didn't need to try and make him remove it for it to be a very advanced technique no beginner could do.