1) Fast-foward the tape to the last 10 minutes of the pilot (possibly the episode Day One).

2) Watch for the scene where Carter lays down on the waiting room chairs and Jerry trying to tell him not to and just gives up. Carter takes off his stethoscope.

3) The camera will switch to the admit desk with Greene walking through the door, Jerry will mention he has a sore throat. Greene says something and keeps walking, as he walks, you can clearly see Carter sitting up again just like before he laid down, With is stethoscope around his neck.

They probably shot the Carter sleeping scene after Greene walking past the desk, but in editing didn't notice Carter in the background.