Visible crew/equipment: You can see the tape marker on the floor where J.D. and the other Doctor are supposed to run into each other. (00:25:30)
Continuity mistake: The pen on the counter Dr. Casey used changes positions a couple of times while talking to J.D. (00:17:15)
Continuity mistake: Dr. Casey's sandwich has a red topped tooth pick in it, but disappears from the sandwich in next shot to the side of his plate without seeing him taking it out. (00:12:45)
Visible crew/equipment: When Ted walks past J.D. and the Janitor you can see the mic on top in middle of screen. (00:09:05)
Visible crew/equipment: When Dr.Cox leaves the room you can see the boom mic in the top of the window of door glass and then it goes up and disappears out of frame. (00:06:15)
Continuity mistake: The napkin on Dr. Casey's cup turns a quarter turn while talking to Elliot before he gets up from the table. (00:12:45)
Answer: No, it was a fake, they used a stamp.
It is real.