Continuity mistake: When Dr Cox throws JD's TV remote on the table, it lands upside down near to the magazine on the middle of the table. However, the next shot of the table shows the TV remote facing the right way up and near the corner of the table. Also the magazine seems to have moved slightly away from JD's beer. (00:18:20 - 00:18:55)
Continuity mistake: When The Janitor and Kelso sits at the bench and Kelso gets up and walks away the bench has straps attached to it lifting it up. The straps weren't there earlier.
Answer: No, it was a fake, they used a stamp.
It is real.