Plot hole: In the season 5 episode "My Fallen Idol", it is a key plot point that Turk has a hard time hugging guys. However in the Season 3 episode "My American Girl" Turk openly gives another surgeon a hug after J.D. makes fun of him. It is not possible for him to have changed because it shows that even before they became doctors, Turk would not hug J.D.
Continuity mistake: In episode 6-12 "My Fishbowl," the janitor waits outside a door holding a fishbowl. The door opens into the room as seen several times. You can even see that the hinges are set up to open in. When the janitor sets the fish bowl down you can see that the door has changed and opens out into the hall.
Deliberate mistake: In one of the later episodes of season 2 Turk is seen being bored in surgery and checking the patient's wristwatch to see how long they have been operating. Patients are not allowed to wear jewelry or watches during surgery as there is a VERY high risk of infection and it might kill them.
Continuity mistake: When Carla and Turk tell JD that he is around them all the time, it cuts to a scene with Carla and Turk in the tub while JD is using the toilet. It cuts back to JD saying "And here I thought that was a lovely evening" while he is holding a bowl of popcorn in his hands. When it cuts the bowl is suddenly on the table.