As you know, Gary, I love TOS, but...
But there are things about it that bother me. The ingrained sexism, as described by Kythe, is a problem. I can usually overlook it, but not always.
A bigger problem for me is the almost total lack of character development. There is some for Spock, I guess, and some for the secondary characters (though damn little), but nobody else. The Kirk, the McCoy, the Scotty that we see at the end of season 3 are the same as they were early in season 1. In fact, the Federation we see at the end is identical to the one we were introduced to in the beginning.
Now, I don't entirely blame TOS for this - I don't think you saw much character development on any adventure show of the time, or many shows of any genre, period. But I really do think that's one of the things that dates the show, at least as much as the special effects, and maybe more. They did the best they could with the special effects. They could have done better with character development.
Another thing that bothers me these days is how so many of the episodes include what I'll call stock elements. For example: heavy-handed morals; cute girls who fall in love with Kirk - and as we know, it is almost always Kirk - at the drop of a hat; female crew members who act like simpering love-sick idiots instead of Starfleet officers (Nurse Chapel mooning after Spock, Carolyn mooning after Apollo, and worst of all, Marla mooning after Khan, an authentic genocidal whacko); societies that are ridiculously Earth-like; societies in which some sort of super computer thingy controls the society; Kirk getting in fights and being picturesquely injured; Spock managing to hide the fact that he has pointed ears and slanted eyebrows by cleverly wearing a hat; and of course those sometimes funny but sometimes stupid little jokes right at the very end of episodes that should not have ended with a joke.
And I know it's heretical to criticise the Big Three, and I don't mean to, but early on I got really tired of That Scene between McCoy and Spock. You know which one I mean: Kirk is in jeopardy, Spock reacts logically, McCoy gets irate and implies that Spock doesn't care at all about his dear friend because Spock has no emotions, and this is even though McCoy has to know perfectly well (from previous episodes) that Spock does care. At age 10, I'm like, "Why does McCoy say that every time even though he has to know it isn't true?"
It's faked-up drama - in fact, a lot of that stuff is faked-up drama. Trek didn't need it, but it used it.
Whew - that sounds a lot more critical than I really feel. I do still enjoy the show, and it has a special place in my heart, but I find that I enjoy it more if I take it episode by episode. That way, I don't expect character development - I just sit back and enjoy the ride.