Probably my favorite of the original Trek episodes. It's a parallel world episode to once again cover up a small budget. All we see are Vasquez Rocks and some interior sets, and they even get around not having to include an audience at the televised games by having fake sound effects for the audience.
So they're clever in getting around the budgeting problems, although the episode does rather feel repetitive if for no other reason then that the landing party gets captured at least three times.
This episode is differentiated from the other parallel world episodes in that this one is more of a "what if"? "Piece of the Action" and "Patterns of Force" are just "Let's visit these 20th century societies." B&C explores what you'd get with Rome _advanced_ to the 20th century. That helps the audience skim over the fact that the parallels here make no sense, that all of the deity names are absolutely identical from those on Earth. Huh?
What really sets this episode aside as unique is that... Kirk doesn't win. The Enterprise doesn't dramatically rescue the last survivors of the Beagle (heck, Merik would still be alive if Kirk hadn't shown up). Kirk doesn't lead a slave rebellion. Yes, there's vague intimations that history will repeat itself and the Roman Empire will fall (although Christianity wasn't the only factor in Rome's downfall).
The fun part is watching Kirk being outsmarted and outclassed at every turn. Logan Ramsey portrays an excellently slimy villain... except he's not really a villain. He's drawn in a few too dimensions to be a flat bad guy (unlike Melakon in "Patterns of Force"). he gives Kirk his "last meal," he offers them a quick death once it becomes clear Kirk isn't going to yield. He doesn't like Merik, but who can blame him? The Proconsul is fighting to preserve his world... and if he can have a little fun along the way, what the heck. Watch him twirl the dagger as the landing party beams away at the end.
So you've got this 20th century Roman who is able to hold off Kirk and his crew and he basically "wins." That gives him a better track record then the Romulans and Klingons combined: see what I mean about him being an excellent bad guy.
As portrayed by the underrated William Smithers, another of those "Hey it's that guy!" faces of the 60s, Merik is a tortured guy who realizes too late exactly what he's sold his soul for.
Shatner gives a decent performance, and of course, McCoy and Spock get some decent scenes, and this episode really shows how they both bicker so much... and can still consider each other friends. The rest of the cast such as it is--Septimus, Flavius, the Master of the Games--are good with what relatively little they're given to do.
The main plot hole is how the heck do they plan to get 427 crewmen to beam down? Prime Directive or not, one imagines poor Scotty with a skeleton crew sitting in orbit, wondering what to do about the 300 or so crewmen they sent down in the last few days...
I think some people underrate this episode because not much happens. It's just another "parallel Earth world" episode. Kirk gets captured, and freed, and captured, and captured, but never really does much. If you look at the differences, though, it's clear this episode actually stands some of those "standards" on their head. This world isn't the same as other parallel worlds, and the fact that Kirk doesn't "win" is intentional. Plus it's an interesting world that we don't see enough of (due to the low budget--we see more of the setting in "Patterns" and "A Piece." Check out the Next Gen novel where the Romans become members of the Federation.