This episode is far from a series classic, but at the same time, it plays out as one of the shaky third season's better offerings, which a decent story and reasonable performances. Indeed, it deserves to be, as it is written by Jerome Bixby, who was behind favourites such as the second season's classic "Mirror, Mirror".
In the US, the episode was originally broadcast on St. Valentine's Day 1969, and I wonder if it was deliberately picked for such, as it is a very romance based story.
This episode is one of just a couple that barely features the Enterprise at all (the other example I can think of being the first season's "The Devil in the Dark"). Instead, the episode plays out on the planet below.
I do agree with some other reviewers that with such a deadly plague raging on the Enterprise, more crewmen would have beamed down to look for the cure, but that is a minor plot point to be overlooked for sake of the story. Flint's floating robot reminded me of the one from the second season episode "The Changeling", but thankfully the story went in a different direction.
In one of the most notable instances of a matte painting being recycled, the exterior shot of Flint's caste is reused from one of the fantasy sequences in "The Cage" (note that I am reviewing the original version; I understand that it has been changed in the remastered version).
Also as has been commented, despite the fact that his crew are about to die a terrible death from disease, Kirk spends no time falling in love with Rayna. We've seen similar in previous episodes of the similar, and again, is just one of those plot points we have to accept.
The story moves along well (I, like others, enjoyed Spock playing the waltz on the piano, for example), and has an unexpected twist about Flint.
The final scene on board the Enterprise, with Spock, McCoy and the sleeping Kirk, is one of the best moments of the third season, ending with Spock's almost haunting "forget".
This is by no means one of the best episodes of the Original Series when compared to some of the other greats, but it probably is one of the best of the weak third season. I cam easily imagine it being part of the (superior) first or second season, where it would no doubt have fared even better.