Other mistake: Spock records a log entry as the "second officer". It appears they got "first officer" confused with "second in command." (00:36:15)
Other mistake: On some VHS editions of this episode, the back cover features a picture of what appears to be both good and evil Kirk sitting at a table, however this never happens anywhere in the episode. That picture is actually from the episode "What Are Little Girls Made Of?"
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