Everybody has his own Star Trek. I give "Who Mourns" high marks, myself. The music is great, Michael Forest and Leslie Parrish are fantastic, and Shatner is in top form as Kirk.
Also regarding the guest stars: the cinematography that captures their striking looks is rich and vivid. You'll never see this on Adam-12. "Who Mourns" is more like a painted masterpiece.
Fred Steiner, who composed the score, liked this episode too and said so.
A missed opportunity might have been exploring more crewmen who'd really want to worship Apollo, but the episode was limited to 50 minutes. The story isn't really bad, nor lacking per se, but easily could have done a lot more - the premise is oddly simple but also allowing complex detail under its surface: Does Kirk really speak so readily for all the crew? How many might want to worship Apollo, and - once defeated because this is Kirk - how would he treat the situation? Not even sneak on down - is the bridge keeping the crew in the dark regarding the big ol' hand that's clasping the hull? (Must be a fun day for the janitors in the bathrooms too... hallways, too...) Most of their missions or experiences aren't this extraordinary. Or wouldn't be in real life, but the show would be far less exciting if - for seventy-eight other episodes - all they did was just show a starfield on a screen for ~65.8333333 hours?