Troy's ability to fix plumbing problems, despite no training, is a parody of the film "Good Will Hunting" in which Matt Damon plays a character who has a brilliant mind for math despite having no formal education.
Troy mocks Abed for using a line from Good Will Hunting about wishing that his best friend would suddenly disappear. In the film, the line is spoken by Ben Affleck who also co-wrote the script. Earlier in the season, Jeff mentions that Ben Affleck winning an academy award for screen writing (which was for Good Will Hunting) was absurd.
After Shirley (Yvette Nicole Brown) says "Dile, Troy" (Tell her, Troy!), Pierce (Chevy Chase) says "Tierra Del Fuego" (Land of fire). Tierra Del Fuego is a Province from Argentina. Its capital is the southernmost city in the world (Ushuaia).
Chevy Chase (Pierce) says "sierra del fuego" faking that he speaks Spanish. In the movie Fletch, he says the same thing speaking to the Spanish speaking staff at the country club after they deliver food to the bungalow.
When Jeff sees Chang destroying his car, he asks him about the safety goggles he is wearing to which Chang replies "safety first." This is an indirect reference to criticisms of the paintball episode which had the characters not wearing safety goggles or ear protection; in paintball competitions, it's a requirement.