A couple of random notes:
1) "Orbit" today is valid parlance for the pattern an aircraft maintains, for example when aiming a radar at the ground below, or waiting for its turn to land, or waiting for a chance to provide fuel to other aircraft. Thus, if Kirk orders a stationary orbit above London, there's nothing semantically wrong with it, even though "stationary orbit" does have other usages in aeronautics jargon besides "staying put above said spot".
2) I think we can all agree that a starship would be able to maintain a steady one gee of acceleration (and thus hover over any given spot) for at least a couple of months if not years. That is, the ship isn't likely to run out of fuel or energy in that time, and the engines supposedly don't require all that much "must take 'em offline" maintenance. Perhaps impulse engines do require some sort of propellant that would run out if the ship wasn't allowed to take short breaks for replenishment, though? Difficult to tell, since their actual method of operation has been kept hidden in aired Trek.
3) The effects of impulse hovering on the spot beneath might not be all that severe when we consider that the shipwrights would do everything in their power to minimize the "impulse signature" anyway, for tactical reasons.