This is very much an episode of two halves. The first half is a drama as the Andromeda-ains take over the Enterprise and keep the crew at bay with their paralysing rays. Later on, things become a comedy.
I like the respect that Rojan has for Captain Kirk. It reminds me of the respect that the Romulan Commander had for Kirk in the classic first season episode "Balance of Terror".
The Andromedians (or however you'd term them) turning crewmen into cuboctahedreal blocks of chalk is an interesting threat. It is unusual that a female crewmember is the subject of such a death, and the moment when Rojan crushes her block up into dust is quite chilling.
There is some nice continuity as Kirk mentions that the Enterprise has already been at the galaxy (in the first season episode "Where No Man Has Gone Before"), and also mentions Spock's previous use of telepathy ("A Taste of Armageddon", also in the first season). It is touches like this that give the series more depth.
Presumably Rojan had a great many more people to take over the Enterprise than we see on-screen. We only see a couple of them, and even with their paralysis rays, it would surely have taken many more to seize command of the ship.
(Without meaning to sound chauvinist) Kelinda is one of the loveliest women seen in the Original Series. Of course, Captain Kirk has to seduce her! I think it must have been part of William Shatner's contract that he had to seduce a gorgeous woman at least two out of every three episodes!
As I say, the second half of the episode goes from being a drama to a comedy, as Kirk and co. set out to 'over-stimulate' Rojan and his people. The comedy highlight – and one of the best sequences of the second season – is as Scotty sets out to get one of the beings stone drunk, and literally drinks him under the table.
One thing that I did wonder is what happened to the modifications that the beings made to the Enterprise's engines to make it faster. Surely the Federation could have made use of this advanced engineering, but what becomes of it is never explained. Maybe it was found to be too unstable for regular space travel?
This isn't an outstanding episode, but none-the-less still has some very good moments and concepts, and makes for a good story.