Kirk tells Spock, "Hold us in a fixed orbit". But Spock is not in control of the ship's navigational controls. That would be the helmsman.
No explanation is ever given for why this planet's landmasses are an exact duplicate of those on Earth.
Although the children haven't physically aged, the sheer enormity of having to care for themselves and one another for centuries would
have left them acting much less like children and more like adults, something we see a little in Miri, but that's all.
When Rand is tied to a chair, the rope tying her there changes position between the long and close shots.
The landing party is out of contact with the Enterprise for two days because of the missing communicators.
Wouldn't the Enterprise notice at some point and beam down some more, or make some other attempt to contact Kirk & Co.?
Although the stardate system was introduced to not give an
actual year date for "Star Trek", Mr. Spock's estimation
that the televison set in Miri's house is three hundred
years old puts "Star Trek" in the 23rd century. (1960 + 300
The guards are out on patrol when the children steal the communicators - how did the kids get the guards' communicators?