I'm surprised nobody has mentioned Gene's treatment of women on the show. Short of one attempt to put Uhura in command TOS has a tendency to be fairly misogynistic and reductionist in regards to women. Surprising considering how in touch Gene was with messages of racial equality.
I think he gets somewhat of a pass on that considering he did originally have a woman as XO in The Cage
and Tasha Yar as security chief in TNG.
To be honest, while the symbolism
of having a female second-in-command in "The Cage" was excellent, I'm not sure that sexual equality was entirely Roddenberry's modus operandi in writing that character. It was more a case of promising his girlfriend she'd have a major (or indeed, a 'Majel'
) role in his series. And when that didn't pan out, he parachuted her in as Nurse Chapel. Nepotism will get you everywhere
I'll give you that Tasha Yar was
progressive, in thought. But not so much in execution.