In the Season 2 thread, I said that many of my favourites are influenced by my first watching as a child which is why I am saving "Spock's Brain". The scenes where McCoy "learns" how to do the necessary brain surgery, and then "forgets" part way through and has to be helped by Spock really stuck out. The remote-controlled Spock has not stood up quite as well (but they did the same thing in DS9 so it's not the concept so much as the 1960s execution that's the problem)
I'd rewatched this episode and it's amazing how long it holds its own before remote control walkie talkie Spock beams down.
Uhura gets to ask the most important question as nobody else was thinking it, proving that brainstorming and committee meetings can be good. For more on this, see 176 episodes of TNG.
The three planets set up (via a great use of a rear projection screen, sadly never to be used again) all have a story being told (and perhaps one
to tell, too) and the unspoken hunch as to why planet 6 is the correct one is thought out really well: The first two given emphasis on having active civilizations, the third seems glacial and dead but that ties into Uhura's question. A hunch indeed.
Then we have the planet of the go-go dancers, using a biological brain as a glorified HVAC unit*, donning the machine and forgetting halfway in just for Spock to
talk the rest of the way through it and downhill the story goes.
With all that said, the POV of Spock - not realizing where he is, just that he's regulating temperature, pumping water, purifying air, etc, and thinking nothing more of that than anything else, is genuinely novel. Plus, the hunch (?) that planet 6 was a civilization that had come and gone is also compelling and, for all anyone knows, may have been the progenitor for planets 3 and 4. The story's a mixed bag, but still has a lot of interesting facets and nuances despite what doesn't work.
* which doesn't explain WHY they needed a biological brain as opposed to any off-the-shelf computer, but in 1968 most computers were still giant mainframes... apart from the tricorders, PADD equivalents, and so on... but, for 1968, it's a genuinely creative and clever idea. So glorified temperature control aside, what would make a brain better than an electronic analogue of one?