When the group is remembering the crazy things Chang has done, Chang is shown snorting corn chips and he says "I said hot damn!"
This is a reference to Uma Thurman's character snorting cocaine in Pulp Fiction (1994).
Annie reacts to Abed's impression of Don Draper of Mad Men. Alison Brie played Trudy on Mad Men (2007).
During the flashbacks showing Chang doing crazy things, Annie walks in on Chang who says he's predicting future crimes. Garrett is shown being forced to lay with multiple leads connected to him, floating in a pool. Chang is trying to prove that Garrett is a "pre-cog" This is a reference to the film Minority Report (2002) in which "pre-cogs" are mutants with the ability to see future crimes and are used as a means to prevent them.
Dr. Heidi says, "I think I've heard everything I need to hear in order to make a decision." Guest star John Hodgman often says something similar as he prepares to decide the verdict in his "Judge John Hodgman" podcast.