I watched Star Trek: The Original Series in order; you can too http://arstechnica.com/?p=458209

The women

Speaking of a different world, there was one big barrier to entry into TOS: its ladies. I'm still not quite sure how to deal with the way women were treated in the show. I've found that when watching many movies or shows from the '60s and '70s, it's incredibly hard to relate the characters—not just because plot pacing was slower and diction was different than it is on TV today, but because I'm almost guaranteed to be disappointed by the way the story treats women. Generally, one just has to accept that there is going to be out-and-out sexism in a lot of old movies and TV, and you can either toss out the whole thing or watch it from afar like you're in a museum, analyzing an ancient culture.

Enlarge / Uhura's character was a breath of fresh air in the Original Series world.

CBS

At the beginning, this is how I approached The Original Series. Despite how much everyone wants to talk about Star Trek's progressiveness in 1966, you can tell just by a quick glance at the costuming that womankind is not going to be treated as equal, with all the rights and responsibilities pertaining thereto.
But around the end of season one, I couldn't help but become a little bit invested in the world of the Federation. I was always happy when Lieutenant Uhura was given real lines in an episode, because she was just what you'd want in a starship officer of the future—brave and serious, but with a human side, too. Nurse Chapel was also welcome—she had gravitas without being robotic and cold.
Of course, for every Uhura or Chapel there was the endless supply of one-off Kirk foils planted on every strange new world, waiting for a strong-jawed spaceman to rescue them. Sometimes they were decent characters, like Edith Keeler in “The City on the Edge of Forever,” one of The Original Series' most famous episodes. In it, Kirk and Spock end up in the 1930s and a depression-era charity worker—Keeler, portrayed by Joan freaking Collins—preaches futurism to a group of unenlightened hobos. (And then Kirk falls in love with her. Because of course.)

 
http://en.memory-alpha.wikia.com/wiki/The_City_on_the_Edge_of_Forever_%28episode%29

Other characters were worse—you need only search “Women Star Trek Original Series” to find the lists of the show's hottest, most vacant babes.

Enlarge / This episode was called "What are little girls made of?" (Spock might answer that human females are carbon-based life forms.) In it, Nurse Chapel's former fiancé, Dr. Roger Korby, commands Andrea the android to kiss Kirk in a scene that is so, so awkward and gratuitous.

CBS

Still, I might have at least given the entire Original Series an “A for effort” if feminism was not so perilously betrayed in the last episode of the third season—"The Turnabout Intruder." The third and last season is famous for just how bad the episodes in it are, mostly due to the withdrawal of both Gene Roddenberry and Gene L. Coon from the show and also by NBC slashing Star Trek's budget dramatically. But to me, as a Star Trek newcomer, “Intruder” was so bad it almost single-handedly negated anything good that the series had put forward in the previous 78 episodes.

Enlarge / Dr. Janice Lester, maniac female, and a man who commands a ship.

"The Turnabout Intruder" sees Captain Kirk switching bodies with mad scientist and scorned woman Dr. Janice Lester, who can't control the ship in Kirk's body because she's too emotional and vindictive. Although Captain Kirk admits at the beginning of the episode that it's not fair that women “can't become starship captains,” (which was news to me although I had just finished almost 67 hours of living in the Star Trek world), the rest of the episode trips over itself trying to show that women really shouldn't be in positions of power—they're hysterical and dark creatures that want what they want without thinking about their responsibilities to those around them.
When the episode finally ended, I was surprised to find that I was glad the whole series was done. I had just spent the better part of two years becoming accustomed to these characters and their flaws and habits, and all the while I was able to believe that the more uncomfortably sexist moments were merely embarrassing holdovers from antiquity, things that the real world and the Federation would eventually figure out. But with that last episode I was done being a Star Trek apologist; I spent a good few weeks trashing it to friends, angry that it had turned on me so quickly.
But absence makes the heart grow fonder, and I eventually capped off my TOS run by watching the movies, and later, a number of episodes from the animated series.