Star Trek's longest title has a double meaning, referring literally to a "strange new world" the Enterprise encounters and figuratively to Dr. McCoy's endangered life. The idea of marrying a science fiction concept to a more personal story is a tried and true formula, but unfortunately here they get in each other's way.... which is a shame, because there's so much potential in both stories.
For obvious reasons, the show has never had one of its characters terminally ill, and the idea of Kirk and Spock coming to terms with having to say goodbye to McCoy is rife with drama. But, the whole situation is rushed, with McCoy declaring his illness offhand in the first few minutes of the show, and the resolution coming equally offhand in the last few minutes.
Most of the episode, however, takes place on an intergenerational spaceship, which is an idea Star Trek previously touches on in "By Any Other Name". Here, writer Rik Vollaerts digs a little deeper, with the episode even including a cute cameo by Jon Lormer, whose character talks about discovering the truth of his world and "touching the sky". (As he tells his tale, the episode slyly includes the same music that plays in the background of his appearance in the show's original pilot, where he plays the fictitious colony leader who introduces Vina). Unfortunately, Vollaerts throws in the old "malfunctioning supercomputer" to serve as the antagonist, which takes some of the emphasis off of the spaceship-world's people and gives Kirk a simple task to solve everyone's problems. ("What's that Spock? There's a computer controlling its people, and we have to take it down? I'm on my way!") In the end, the episode ends up less about the intergenerational ship or even the developing romance between McCoy and the its leader, Natira, instead being more about "Kirk and Spock versus the machine". (Truth be told, McCoy and Natira have little chemistry anyway, with DeForest Kelley, for some reason, not even smiling in his scenes with guest star Katherine Woodville. He probably knows, however, that the writers have shortchanged the scenes between the two, providing no foundation for their relationship and making it difficult to for any audience to buy that McCoy wants to stay with her whatever he does with the character).
All the same, at least the episode has some bold ideas... and good ones at that, making it watchable and somewhat memorable. (It's sort of like "The Paradise Syndrome" from the asteroid's point of view). And heck, it's good to see McCoy finally get the girl!
Curiously, the episode even leaves open the possibility for a sequel, with "Ex Machina", a Star Trek novel by Christopher Bennett published in 2005, unofficially tying up the loose thread.