Continuity mistake: In the apartment there is a cardboard box on a table, with a strip of blue tape on it and a tube of paper sticking out of it. A few shots later another strip of blue tape suddenly appears on the box and the tube of paper has vanished. (00:02:35 - 00:03:15)
Continuity mistake: When Dr Cox is watching TV, a guy in green walks past the people in the background, the camera goes to a close up of the doctor with the remote and the same guy walks past again.
Answer: No, it was a fake, they used a stamp.
It is real.