Phil noted in the DS9 Nitpickers' guide that the station sometimes rotates, sometimes doesn't, as though someone somewhere has a control to turn it on and off.

In the episode "After Images", Ezri says she can feel the station rotating.

So, does that mean that Ezri can tell when the station stops and starts turning? If so, she should report the problem to Chief O'Brien!

I don't see why the station should rotate, to begin with, because a docked ship of significant tonnage compared to the station would strain the docking ports more than a light ship. Any object would want to go in a straight line, but if it isn't firmly attached to the station, it would rip away to keep going in that straight line while the docking port rotates away.

If the station does rotate, there must be supplementary systems that use energy, not mere physical clamps, to hold a ship firmly in place while it is constantly forced to change its inertial vector.

Of course, the slower the station rotates, the less strain there would be.

I hope no ships were docked with the station when O'Brien moved it from Bajor to the Wormhole, since it was entirely voluntary. As long as the station wasn't rotating, at least once they get under way, everything's moving in a straight line.
But when one of Vash's artifacts was trying to get "home", any ship docked to the station just might have been in trouble unless it disengaged.

The episode was "Afterimage."