After reading everyone's interesting and thoughtful posts, I thought I'd chime in with a few observations. I'll let the pictures carry the weight, since pictures are always fun and instructive.

I wonder if the Karidian Company of Players carry with them their own sets? They wouldn't be showing much 'thanks' to the crew if they had to earn their performance by toiling away with saws and paint!

Someone mentioned Lenore's many costume changes. I'd never paid much attention to it, but they're right! I wonder now if she holds the Star Trek record for most costume changes? I don't even think France Nuyen had this many.
By the way, that observation deck had only this one appearance, but it sure left an impression. Who among us didn't visualize this very place in our heads when Sarek spoke of it in his 'private meditation talk' in
Journey to Babel?

This is a meaningless observation, but that woman seated in the back doesn't look like she belongs there. What I mean is...well, she doesn't even really look like a 1960's person (whatever that's supposed to be)! Maybe it's just that she isn't an actress, or something like that. At least we see her, unlike...

That's about the most we see of the other party guests. Speaking of that, who'd go to this party? I'm not aware that they knew anyone on the planet. Is it some sort of traditional function in the theater world? And what if there are other colonies on this world? If you happen to be a theater lover, and happen to live in another settlement where the Karidian Players didn't perform, sucks to be you, I guess.

Was it wise to move Tom Leighton's body? I didn't get the sense that there had been any kind of investigation between the scenes pictured. There must be some kind of law enforcement apparatus on the planet, or are visiting starfleet officers automatically the big shots?
The rec room was the most boring place on the ship. How can you have any fun in there? There's that computer thingie on that table, but it looks a lot like a piece of work hardware to me. Well, there's always three dimensional chess. No, wait...what happened to the chess pieces? Is this right after
Charlie X, and they hadn't gotten around to replacing the ones he'd melted yet? Luckily, Uhura planned ahead for her trip, and brought her own entertainment!

But all in all, people from the 23rd century are no different than you or me: Just turn on the tv, and they'll plop themselves down for hours!

To me this is the "iconic" image in my head when I think of this episode.

Any more thoughts about this thing? I can't figure out what it's for...and it strikes me as odd that it just happens to be so close to the captain's quarters. Was this vent ever spotted again in background corridor?

At first glance, this looks rather dated. But maybe by Star Trek time, only paper documents are considered legally valid? But it also makes me wonder what happened to that voice test of Karidian that Kirk took. You do have to admire Kirk, though: The torturous Tarsus IV experience of his youth, and with circumstantial evidence now mounting against Karidian, Kirk wanted, as he even said himself, to be absolutely sure.

The actor next to Arnold Moss really poured himself into his small role!

I'm far, far from an expert on hostage situations and such, but could not one of these able-bodied crewmen and women have helped out somehow?