Continuity mistake: When Dr.Kelso steps on J.D's paperwork the papers under right foot change positions. (00:15:25)
Continuity mistake: When Dr. Kelso is chewing out JD, the amount of banana peel hanging out of JD's pocket changes from shot to shot.
Character mistake: JD is having problems with someone dressed in a gorilla suit, who is slightly shorter than he is. JD sees the janitor, who is considerably taller than he is, eating a banana and accuses him of being the gorilla. If the janitor were as tall as JD, maybe, but you would not confuse someone shorter than you with someone taller, regardless of costume.
Answer: No, it was a fake, they used a stamp.
It is real.