The episode does have its own wholly internal chronology/continuity problems. If Kirk has known Mitchell for fifteen years, but Mitchell first met a "Lieutenant" Kirk at the Academy, then both men are about the age of the actors portraying them - yet the onscreen graphics try to suggest Mitchell is but 23 years old.
I don't see the upside of pretending that Mitchell is 23 or Dehner 21, but apparently youth was directly related to sex appeal back then in a rather embarrassing way. At least Michael J. Fox sort of looked the part...
My assumption is that those were records made when they joined up after graduating the academy, not reports of measurements made earlier that day. I assume cadets ESPer rating is measured and noted during their training and these are the documents we're seeing on screen.
As for set differences, my understanding is that both pilot episodes were filmed in one studio and then the sets were half struck and carted over to a different, larger studio somewhere else in town. Off the top of my head, I want to say the pilots were made at Desilu in Culver City and then moved to Paramount? It's been a while since I looked any of that stuff up so I probably have that mixed up and rearranged somehow, but the pilot episodes were definitely made in a different place than the series production was. That's why there are so many differences in the set details, and more sets for the series.