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.
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.
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.
Factual error: A kid is being taken to surgery to remove a magnet he swallowed because it may be stuck in his upper intestine. House diagnoses that the magnet is already in the lower intestine by taking a scalpel and showing that it's magnetically attracted to the lower abdomen. Surgical scalpels are made of high grade stainless steel and are not attracted by magnets.
Plot hole: When Wilson does an ultrasound to check for cancer in Alex' ovaries he fails to notice the fact that she doesn't have a uterus. If he mistook her bladder for her uterus, which sometimes happens, she would have appeared to be missing her bladder instead. Yet Wilson doesn't pick up on anything being missing.