Continuity mistake: As House describes the lady's symptoms, in the front shot Chase has a small book/pamphlet in his hand. The camera changes to a side shot in the middle of House's description and suddenly the book is on the table and no longer in Chase's hand. This happens right in the middle of House's line and Chase doesn't make any quick movements to account for this discrepancy.
Factual error: House is playing 'Metroid: Zero Mission' on his Gameboy at various times. The Metroid series does not feature space monkeys, nor are there distinct levels. The sounds coming from the game in the show do not match it in real life, and Samus morphing into a ball is most definitely not a failure state.
Character mistake: Episode 6.12, Moving The Chains: Marcus tells House that he and Eric were arrested for stealing a car, he was 16 and Eric was 14. He also says that his brother never did anything criminal after that. In season 1, we were told that Eric was 16 when he was arrested for stealing a car.
Continuity mistake: House is about to inject Ezra Powell (Joel Grey) with what is supposedly a lethal dose of morphine. In the shots where they pan out to show House addressing the room at large, the syringe is very full, almost completely. When they zoom in on House holding the syringe, it is only filled a fraction of that much - maybe a quarter to a third. This doesn't happen just once, but every time they switch between shots.
Factual error: When House is looking over his whiteboard of symptoms for the swimming patient, the symptom "Intercranial Hemorrhage" is shown on the board. However, this is an error. The correct term is "Intracranial Hemorrhage." Anything inside the head is referred to as "intra" not "inter." This is a common mistake for laypeople, however the highly trained and knowledgeable Dr. House should not have made that error.