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.
Plot hole: In the scene with Mikey in the NICU, the alarms start to go off, stating that he is in distress. The nurse screams "He's in V-fib!" and everyone rushes around him. In the next shot they show the heart monitor just before Chase shocks Mikey's heart. The problem is that the heart rate is so fast with one wide complex that it would actually be Supraventricular Tachycardia with 1 Premature Ventricular Contraction (SVT with 1 PVC), which is far less serious than V-fib and wouldn't require the heart to be shocked.
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.
Continuity mistake: In the beginning of the episode, when Cuddy presents the case to House, she has her cell phone in her left hand when handing him the file. She doesn't have it in her hand when she slides the file closer to him. When the camera faces her, you can see her arms are bent up while talking to him, and see the phone. When the camera is facing House, Cuddy's arms are hanging down by her sides, no phone.