Continuity mistake: Kirk and the others are beamed down to the planet, and when the Enterprise crew are led into Mudd's throne room by two Alice androids (the Alice series are 500 identical androids) they are wearing the usual metallic, backless, kitten heel slip-ons, but in the next shot android Alice at the left is now wearing altogether different shoes - cream color with ankle-straps. (00:09:30)
Visible crew/equipment: A stagehand's foot is visible before the party beams down. (00:09:10)
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