Factual error: In episode 414, "Living the Dream," the patient Evan is given a nerve function test. We see Kutner and Taub performing the test by puncturing Evan's legs with needles. Modern nerve function tests actually rely on electrical impulses from a small computerized device, with no needles necessary.
Continuity mistake: Throughout both parts of season 4's finale ("House's Head" and "Wilson's Heart"), Amber is always shown getting hit from the back and sitting facing House, so her seat's back is to the windows. Yet the last time we see the accident, that is, right after she took the flu pills, she is definitely sitting neatly sideways to the window (i.e. the seat is perpendicular to it) and getting hit from the right side. It most likely was done for artistic reasons, as the back shot, shown multiple times, makes for a very neat effect, with her blonde hair flowing around her like sunrays.
Plot hole: Since the doctors do not know the identity of the patient, Cole and Thirteen are given the car keys they found on the man and instructed to go to the area where he was found and try it in every car door. When House calls them, Thirteen says, "His car was towed and the tow gate's locked." House tells them to break in to the car impound. Given the only way for them to identify the car was using the keys, if the car's been towed away then it wasn't there for them to try the key in the first place.
Other mistake: At the end, before House's "realisation" the camera pans out and shows a street light when House and Wilson are outside talking. The lamp top is covered with fresh snow. It's been dark for sometime. The heat from the bulb would have melted snow had it actually been real.
Continuity mistake: A third of the way into the show when Hadley and House are arguing while walking out of House's office, Hadley's necklace watch is backwards and out of the top of her blouse. When they stop walking and switched to a shot of House then back to Hadley, her necklace watch is right-side front and inside the top of her blouse.