A lot of the women in TOS were far too passive. We're told Chapel is a scientist and yet she fulfills the role of jealous fiancee in her only major episode and she always assists McCoy rather than conducting her own research in later appearances.
Rand was often a bit part and in Miri, although it's one of her larger roles, she does very little to move the plot along. The average Dr Who assistant would have put more effort in to reason with or escape from a bunch of children. I think they laboured a bit too much about their attraction in those early episodes - when Kirk is drunk he pines for her, when she's losing her marbles she tries to show him her scabby legs. Less would have been more! In a modern show they'd have kept the will-they-won't-they thing going for years.
However, there are other episodes where Rand sparkles. I love her interplay with Sulu in the Man Trap, the way she tries to stand up to the drunken Kirk in the Enemy Within, and the interplay in Charlie x. There was a lot of lost potential in her character.
Uhura on the other hand had quite a lot of sass, often portrayed with an imperious look, or arch comment. There were some of her larger episodes where she was bit passive but more often she got stuck in.
Other decent heroines were the impish Helen Noel and the acerbic Ann Mulhall either one of which I would have liked to see again.
I hate to agree with 2takes but I'm thinking maybe he's right about Whitney elevating the writing of Rand. Her role seemed to be to have a crush on the handsome captain and to be saved by him or Spock in various episodes. I liked the way she handled Creman Green in Man Trap and even imploring Spock (in vain) to save her from amorous crewmen in Naked Time showed she wasn't just some some damsel in distress. And even giving Spock the evil eye at the end of Naked Time.
All the good work with the women characters seemed to be spoilt by their embarressing crushes or by saying I'm frightened or holding onto Kirk in stressful situations, or having to be saved by 'men'.
In nuTrek, Uhura and Carol actually contributed to the solution of the problems as much as they could. Not relying on the men to save them.