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)
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.