Continuity mistake: After JD has read the notice on the board Dr Cox talks to him and his clip on his stethoscope goes from digging into his neck, to being pinned under his collar.
Continuity mistake: Laverne's clipboard changes from being held out in one shot to held close to her in another while talking to Dr. Kelso. (00:04:15)
Continuity mistake: Dr. Kelso sets his water bottle down twice while talking to Turk. (00:16:20)
Continuity mistake: At the end, when J.D. has found out he is going to Reno, he turns to gloat to the other residents, and Dr. Cox. Snoop Dog Resident appears both in the group of interns opposite Dr. Cox, as well as directly behind Dr. Cox.
Answer: No, it was a fake, they used a stamp.
It is real.