Continuity mistake: In the episode where Elliot is missing J.D. and talking to him a lot on her phone, he asks her to drop the phone into Dr. Cox's pocket. She drops it into his left coat pocket, but he later pulls it out of his right coat pocket. He couldn't have changed it in his pocket, because he's surprised to find it.
Continuity mistake: In the apartment there is a cardboard box on a table, with a strip of blue tape on it and a tube of paper sticking out of it. A few shots later another strip of blue tape suddenly appears on the box and the tube of paper has vanished. (00:02:35 - 00:03:15)
Continuity mistake: When Turk and Elliott are in the line at the cafeteria, you can see that Turk has two plates on his tray and Elliott has a juice box on her tray. When they turn around at the end of the line Turk has just one plate on his tray and the juice box on Elliott's tray is also gone.