According to House's parallels with Sherlock Holmes, when he challenges his team to solve the puzzle of the diagnosis, he writes it on a piece of paper, puts it in an envelope, and on the envelope writes, "The game is a itchy foot." This is a play on the words of Holmes' famous phrase, "The game is afoot".
House's physical therapist criticizes his use of his cane on the wrong side, although some patients who use a cane long-term will use it on the injured side or on the opposite side. It comes down to personal preference and ease of use, though therapists will always recommend the uninjured side.
"Ralph" is a slang term meaning "vomit," creating a funny coincidence when the kids sing "It's time for Ralphy" just before Jack vomits on their cake.
House says, "Powerful stuff, the O.C. of its day," referencing the TV series Party of Five (1994), starring Matthew Fox, Neve Campbell, Jennifer Love Hewitt, and Lacey Chabert. As noted, it dealt with an older brother raising his brothers and sisters after the death of their parents.
Cassi Thomson (who played Kama Walters in this episode) & Tanner Blaze (who played Will Walters in this episode) both had roles on CSI Miami.