Continuity mistake: Near the end after JD tells the interns he wants them all to wave, they all start waving their arms. The shot cuts to a different view and Rex's hands are instantly back on the table.
Continuity mistake: If you watch when Alex slips on the wet floor, you can see the woman from behind has longish hair, extending past her shoulders. In subsequent episodes we see Alex's hair is much shorter than the one that falls in this episode.
Continuity mistake: When the girl in the bathtub comes crashing through the ceiling, she has her hands covering her upper chest and no bath bubbles. The next shot there is a great deal of bath bubbles all over her and we cannot see her hands covering her chest. As the guy falls through the ceiling, the bubbles on the woman again disappear and we see her hands.
Continuity mistake: When JD is talking to Carla in the cafeteria, she tells him that it's nearly 5:00. But up to that point, you can see the bottom half of the clock behind him and the hour hand is not visible. It only appears after she tells him the time.
Answer: No, it was a fake, they used a stamp.
It is real.