I wasn't going to address this, but I fall squarely in the "not rotating/not orbiting" camp.
In the original episode, we see
apparent rotation of the station and
apparent movement of the ship; but, when seen from the station office, neither the stars nor the Enterprise are moving.
There is a conflict of visual evidence here that must be reconciled. There are two ways of doing this, both of which require ignoring some part of the visual evidence.
One way stacks improbability upon improbability and says that both the station is rotating and the ship "orbiting." The static view from the office is an error. This ignores the unwanted centrifugal effects on the station, the extra difficulty introduced in docking with it, and the massively unnecessary and constant need for the Enterprise (and every other visiting ship) to fly a powered circular path around the station. (Orbiting is simply not possible with the relatively tiny mass of the station. If it were even attempted, the orbital period would be so long that neither the ship nor the station would appear to be in motion to the naked eye; and given the relatively similar masses of the two objects, they would both orbit around a common barycenter, not one around the other.)
The other way supposes the apparent motion is actually
motion of the camera, gliding by the ship and around the station. The ship and station are static and the apparent motion on screen is induced by a moving viewpoint for visual interest. The only error on screen here is that there should be a slight drift of stars in the exterior shots. The view from the station office is entirely correct. Note that the apparent rotation of the station is in the same direction as the apparent "orbit" of the ship. This is the same effect one gets from a camera moving through the scene on a circular path.
This second explanation is by far the simplest and also agrees with the script directions, which specify a
stationary station and ship. David Gerrold even points out the spurious motion in his description of the episode in his book "The Trouble with Tribbles" (1973). From page 177:
TRANSITION SHOT - SPACE STATION
Enterprise hanging motionless nearby.
Footnote: The space station is shown to be rotating slowly -- which is actually unnecessary if you have an artificial gravity.
...and if the space station is rotating, then why was the Enterprise shown motionless through the window of Lurry's office? (Pick, pick, pick...)
Finally, for those who favor the "flying powered circles" around the station, there are a host of issues that are introduced by this, both of physics and logistics. I'll cite just one: If this is standard procedure, how big a mess would you have at a busy time when there are 10 or 15 ships visiting the station, all swooping around it like a cloud of angry bees, each under it's own power? Yikes!
All of this is avoided if we assume a moving camera viewpoint.
M.