Other mistake: Kirk and Spock stun two Klingon guards, yet despite being unconscious, the guard on the left jumps from the balcony and lands feet first on the ground. If he were really unconscious he would have simply tumbled down. (00:36:20)
Other mistake: When Kirk is lecturing Ayelborne in the council chamber, the actor behind him is mouthing Kirk's dialogue.
Chosen answer: If they're in orbit, they're being pulled along by the planet's gravity well, therefore, impulse engines would only be used for minor corrections and would be "on standby" while in orbit, but not active. (Like keeping your car idling without revving the engine and creating plumes of exhaust).
Captain Defenestrator
Thank you for the info.
Movie Nut