Continuity mistake: The defib paddles Dr. Cox uses change from being in the slots, to on top of the machine a couple of times. (00:15:40 - 00:17:10)
Deliberate mistake: When Carla shows Elliot what she looks like in the bedpan and Elliot says she looks like Alice Cooper, you can see her reflection in the bedpan. However the camera is to the side of Elliot's head, so if we can see her reflection, she wouldn't be able to.
Other mistake: In the last shot of the final scene, when JD and Elliot start down the wheelchair ramp outside of the hospital, an "extra" woman walks right in front of them. She was nowhere to be found in front of JD and Elliot before they started walking - she simply appears in front of them and walks down to some paramedics holding a stretcher.
Answer: No, it was a fake, they used a stamp.
It is real.