Spock: Fascinating. This atmosphere is remarkably similar to your 20th century. Moderately industrialized pollution containing substantial amounts of carbon monoxide and partially consumed hydrocarbons.
McCoy: The word was "smog."
Spock: Yes, I believe that was the term. I had no idea you were that much of a historian, Doctor.
McCoy: I am not, Mr. Spock. I was simply trying to stop you from giving us a lecture on the subject.
McCoy: Just once I'd like to be able to land someplace and say, "Behold, I am the Archangel Gabriel".
Spock: I fail to see the humor in that situation, Doctor.
McCoy: Naturally. You could hardly claim to be an angel with those pointed ears, but say you landed someplace with a pitchfork..
Flavius: What do you call those?
Spock: I call them ears.
Flavius: Are you trying to be funny?
McCoy: Quite logical, I'd say, Just as it's logical that a 20th-century Rome would use television to show its gladiator contests or name a new car the Jupiter 8.
Spock: Doctor, if I were able to show emotion, your new infatuation with that term would begin to annoy me.
McCoy: What term? Logic? Medical men are trained in logic, Mr. Spock.
Spock: Really, Doctor, I had no idea they were trained. Watching you, I assumed it was trial and error.
Claudius: I believe you all swear you'll die before you'd violate that Directive. Am I right?
Spock: Quite correct.
McCoy: Must you always be so blasted honest?
Achilles: Stop running! Fight!
Spock: Need any help, Doctor?
McCoy: Whatever gave you that idea?
Achilles: Fight, you pointed-ear freak!
McCoy: You tell him, buster. Of all the completely... ridiculous... illogical questions... I ever heard in my life!
Claudius: Admit it. You find these games frightening, revolting.
Kirk: In some parts of the galaxy, I have seen forms of entertainment that makes this look like a folk dance.
McCoy: Angry, Mr. Spock, or frustrated, perhaps?
Spock: Such emotions are foreign to me, Doctor. I'm merely testing the strength of the door.
McCoy: For the fifteenth time.
Marcus: You're a Roman, Kirk, or you should have been.
Claudius: Would you leave us, Merik? The thoughts of one man to another cannot possibly interest you.
Does Merrick (and thus the Proconsul) really believe they're going to lure all 400+ Enterprise crewmen down to the planet? Apparently they think that after Kirk, Spock, and McCoy are killed, Scotty will send down another recon party... and another recon party... and then even more. Realistically, at some point Scotty's going to say, "Well the last 20 recon parties disappeared... better not send another." But for their plan to work, Merrick and the Proconsul have to ignore this obvious fact.
Even if the landing party doesn't have subcutaneous transponders, and the Romans are biologically identical to humans... Scotty & Co. could still scan for the only Vulcan on the planet, wait until he's isolated, and either beam someone down to investigate or beam him up.
Kirk uses a machine gun to blast the cell door and then swings it open. It is clear that the lock is undamaged; a lock shot open by a machine gun would be torn apart and ruined.
Claudius says he's going to give Kirk a 15-minute televised execution but then tells the Master of the Games to kill the captain with one quick thrust. What are they going to do the other 14 minutes?
They've done it before, but once again they take Spock on a landing party when they're under strict orders not to violate the Prime Directive and give any indication that life exists on other planets.