Continuity mistake: The first time Turk and Cox are talking in the gym, watch the man on the machine behind Cox. During the first shot of Cox, the man's face is obscured by the pulley for a pull down bar. Cut to Turk then back to Cox and the pulley has moved enough so that the man's face is now visible. Cut to Turk and then back to Cox for the third time and the man's face is blocked again. The viewing angle of Cox is the same each time so it is not a camera angle difference.
Continuity mistake: When Carla & Elliott get into the back seat of the vehicle after attempting to hire a male prostitute, you can see them clearly in the close shot. In the next (long) shot, when it is revealed to be a police cruiser, there is a cage between them and the camera. This cage disappears again in the next close shot.
Answer: No, it was a fake, they used a stamp.
It is real.