I'm only counting internal explanations, not the fact it's an old show that they didn't think anyone would care about in 40 years. If the show has plotholes, it has plotholes. When an entire franchise is built upon a series, I won't give it any leeway. It has far too much to answer for in later series.
In the Roman episode, the Starfleet captain didn't bring the Roman influence, they already existed that way with "Roman values", and I'm pretty sure the Jesus guys existed long before they arrived too.
You've got me on the Nazi episode though. I just skimmed it, and they even pointed out there the fact it was impossible it naturally evolved like that. The thing that happens in all these TOS episodes is that they usually only explain these things at the end of the episode as a quick throwaway thing to try and get away with it, so I forget them a lot of the time.
In the case of the gangster planet, and the nazi planet, it is still a ludicrous excuse that one person or book comes along, and an entire planet just 100% embraces it with not the slightest deviation.
All they had on the gangster planet was ONE book. And from that, they had the speech patterns, the clothes, CARS, GUNS, the architecture. There's no denying it's a lazy excuse to go cheap on props and costumes. That kind of transparency really kills those episodes for me for anything but outright humour value.
Off the top of my head, aside from one episode I can think of (the um, old hotel thingy? I hope you know what one I mean
), I don't recall TNG having such blatantly poor explanations for other worlds, or such obvious carbon copies of Earth week after week.