I just finished watching remastered Balance Of Terror; one of the best all time!
I've seen this episode literally dozens of times, but I noticed something that never sunk in before; in the scene where Kirk, Spock and seemingly all the bridge crew, except Uhura leave for the briefing room, Kirk calls back to the bridge and talks to Uhura, for a status check. From what he said to her, one could easily interpret that she had been left in charge.
Interesting . . .