As shown by House, Taub and Thirteen, one of the last refuges of the use of fax machines in the age of email was, and continues to be, the medical profession. This is because security of patient information cannot be guaranteed in emails, but a fax transmission is virtually safe from interception.
House's reference to Dr. Perlmutter is from Clive Cussler's Dirk Pitt novels, popular in the 1980s.
A man in the previous episode "Known Unknowns," dressed as a Ghostbuster, refers to Cuddy as Jane Fonda. In this episode, Troy Garrity, son of Jane Fonda, plays the patient, Hank Hardwick.
At the end, House asks where he can find a "mission accomplished" banner. This is likely a reference to the speech George W. Bush gave on May 1, 2003, during which a "mission accomplished" banner was displayed behind him.
House discusses with Wilson which three of his four potential team members he should hire, and says that a team of five would be unwieldy. After the interview process in season four, House wanted to have a team of five (Foreman, Taub, Kutner, Thirteen, and Amber)--a suggestion that was quickly rejected by Cuddy.