Other mistake: When Turk is squirting cream on to the pancake to make a face, we hear 3 squirts which wouldn't be enough. The eyes are X-shaped and would take 2 each plus the smile would have taken a longer squirt.
Continuity mistake: At the beginning, the doctors do the race to get the board member patient. They take the lift from the 4th floor. When they get out of the lift, they are still on the 4th floor.
Answer: No, it was a fake, they used a stamp.
It is real.