This is one of those mystery episodes where they come up with a cool (and in this case budget saving) premise, but they don't know where to go with it and end up tacking on an ending that doesn't make any sense.
The story itself, conceived by Stanley Adams (Cyrano Jones in "The Trouble with Tribbles"), cleverly contrasts being alone with the claustrophobia of overpopulation (both being something Cyrano Jones would know about). But the story is crying out for a holodeck-like twist (as teased in TNG's "Future Imperfect") and Star Trek isn't far enough along for that yet; instead, as the mystery starts to unravel, we get answers with plot holes you could drive a starship through.
Kirk gets the A story, sharing it with Odona (Sharon Acker) on an empty Enterprise. Moving at a snail's pace, the first half of the show lays out the episode's main ideas and issues as the two converse and the script throws in some super creepy (and effective) reminders of the hell of over population. Acker is okay, though her bizarre bikini print pantsuit makes it clear the wardrobe department is mailing it in, knowing cancellation is around the corner. Shatner is fine as well, though it's interesting to ponder how well this could have worked as an Uhura or Sulu story, with these interesting characters too often overwhelmed by others that they wouldn't have to share the screen with here.
Along with Spock and Scotty, they instead get the predictable B story, the search for the lost captain, but this time it has a clever twist: instead of having to zip around the galaxy or fight battles to find Kirk, they instead have to fight their way through bureaucratic red tape and play a game of semantics with a planetary leader, played by a hammy but hysterical German named David Hurst. Though it's all dialogue, it's actually a lot of fun and, anchored by Nimoy, uses the ensemble well.
About three quarters of the way through, however, the episode hits the wall because it has no good conclusion to go to.
In literal terms, the episode is probably a failure. In thematic and poetic terms, however, it's somewhat interesting... for a while.
This is mostly your basic "new Enterprise and new planet" remastering effort (replacing the original's reuse of "The Deadly Years" footage) - but they do tweak a few other shots. Most notably, they update the chronometer to match the "The Naked Time", which here requires some fancy work due to a panning camera.