Space Seed, TWOK, and STID. Khan is a completely amoral, horrible character with absolutely no redeeming features. And the way Lt. McGivers was treated in Space Seed was disgusting, she wouldn't have betrayed her captain and crewmates no matter how thralled she was by a man. And I absolutely fail to understand why they chose this one if they had to make a feature movie as a sequel to an episode.
The Changeling. I quite like the episode otherwise, but the way NOMAD was confused by Uhura's female brain badly enough to render her unconscious was just the sort of casual sexism that has made TOS age quite poorly. When we watched it with our son, 14 at the time, he was like
Turnabout Intruder. The whole premise that women couldn't be captains is off-putting. Even if the story was well crafted otherwise, the premise utterly ruined it for me. It didn't really help matters that it was the last episode they ever broadcast, even if it wasn't intended as a finale (because the concept of a finale didn't exist then, episodic shows just ended).