Well this is a tricky one to talk about.
Synopsis
The Enterprise pursues a small, unnamed ship into an asteroid thicket. The pursuit damages the Enterprise's lithium crystals (which would later be called dilithium), but they bring the unnamed ship's four inhabitants onboard before it's destroyed: galactic conman Harry Mudd, and three hot chicks.
The women muddle the minds of the male crew members, except Spock. Kirk maintains greater control of his hormones, but speculates on the effects the women have on him too. They need to get to a mining planet to replace the broken lithium crystals before they lose life support. McCoy also wonders about the strange effect the women have on the men, but he doesn't think too hard about it, if you catch my meaning.
Turns out, Mudd has a miracle pill that makes the women hot, and if they don't have it often enough, their hair gets disheveled and they develop facial prostheses that make them ugly. So this is the con: Mudd sells the women to lonely lithium miners, and the "ugly" women get men to marry (since this is definitely how women work).
Mudd has one of his women steal a communicator, and uses it to contact the mining planet ahead of time, saying that he'll trade the women for the lithium—and for them to blackmail Kirk into letting Mudd go. The miners present these terms to Kirk, and he refuses. With limited power, and an even more limited understanding of orbital mechanics, the Enterprise is going to crash into the mining planet in a few days.
One of the women gained a conscience from her own run-ins with Kirk, and wants out of the con. However, she ends up like-liking one of the miners, and he like-likes her back—even without the wonder pill. She berates the miners into giving Kirk the crystals, so Mudd remains in custody... for now!
Commentary
Well.
So first off, the actual message here is that beauty is not skin deep. This is played both ways: the women are ugly without the wonder pill, and the men are, you know, they're miners on an isolated planet.
I kind of like Harry Mudd, because he's an actual scoundrel. This feels like the opposite of the whole "Han shot first!" business, because it doesn't matter who shot first: Han always comes through. Mudd is just a fuck up, and that's refreshing.
The role of sexuality in Star Trek is its own big topic. I do appreciate that Trek isn't sterile and sexless, and maybe the boldness of doing weird stuff like "Mudd's Women" was what gave future writers the space for stuff like Risa and "Justice" and, later on, letting Jadzia Dax be so sexually open.
Or put another way, sex is an important part of humanity, but it's just so icky and we have to worry about ratings and Catholic boycotts and so forth. I'm not sure that Star Trek would have managed the intensity of humanism if we didn't have Data fucking Tasha Yar in "The Naked Now," or Bashir's awkward attempts at flirting with Jadzia and later success with Ezri, or Jadzia's marriage to Worf or even, awkward as it was, Picard "righting past wrongs" (i.e., not fucking Marta) in "Tapestry."
Getting back to Mudd and his women, part of why this is so tricky for me is that I'm a gay man, so I'm pretty far out of the loop on whether any of this makes any sense. I appreciate that there's a surprisingly fine line between "realistic portrayal of people as they actually are" and "boorish chauvinistic fantasy." I am, frankly, not competent to judge this one, so I guess we'll all have to make up our own minds.
