House starts chanting "ATTICA! ATTICA! ATTICA!" while arguing over his office carpet with Cuddy. This refers to the Attica prison riot in 1971, where prisoners took control of the facility after an uprising against the poor conditions, and probably more specifically Al Pacino's chant in the movie "Dog Day Afternoon".
In trying to get rid of Ali, House quotes virtually verbatim Rick Blaine's farewell speech to Ilsa Lund in "Casablanca".
In the cold open, Adam's father asks him to identify a picture of a bicycle from a binder. This is an actual communication system for people with autism and other disorders that affect speech. It is called PECS or Picture Exchange Communication System.
The game that Adam is playing on his PlayStation Portable is Frogger: Helmet Chaos (2005).
When House says, "So, think maybe Gray's Anatomy got it all wrong?" he sarcastically alluded that Adam's liver cells were in the right place and Henry Gray's Anatomy of the Human Body, one of the most reliable and comprehensive resources used by medical students and professionals, got the placement wrong.