The amount of snow on Anica's head and shoulders as she talks to House on the bench outside the hospital changes significantly between shots as the conversation unfolds.
When Cushing's Syndrome is brought up, the patient states that she, "had it last year," insinuating that it had been cured, that she no longer had it. Cushing's Syndrome is an ongoing condition, whose symptoms can be mitigated, but it can't really be 'cured,' or gotten rid of for good, so if she 'had it last year,' she would still have it now.
At the end of the episode - which takes place in the winter, at Christmastime - House puts in a wager on a race at Belmont Park. Belmont Park is never open at that time of year. If he was looking to wager on a New York racetrack at that time of year, it would be Aqueduct.
In the opening scene at the OTB, House bets on a race at Gulfstream Park (which is in Florida). The beginning of the race, as shown on a television in the parlor, is from Gulfstream Park, but all other race clips shown - which are supposed to be the same race - are from Santa Anita (which is in California).
When House talks about his "inside information," he mentions that the jockey purges at the starting gate so that he will weigh less during the race. For one, the jockey "weighs out" before the race and "weighs in" after the race (this is incorrectly stated by House). If a jockey was found to be two pounds less than his assigned weight, he and his horse would be disqualified (a small amount of weight loss for sweat is allowed).