Jim Kirk gets his own Dances With Wolves adventure in a story that spans two months, making this one of TOS's most unique episodes. But what used to be considered a third season gem is less popular today with audiences are more aware and less tolerant of Native American caricatures. (Poor Disney has it worse, with its 1953 Peter Pan movie having an entire song asking "What made the Red Man red?" while an old Native American gives the kids a peace pipe to pass around).
The idea here is similar to TNG's Magna Opus, "The Inner Light": the captain gets to have everything his starship denies him, gaining a life with simple and stable pleasures free of the burdens and responsibilities of command... at least until the world is threatened. (It is, ironically, the same sort of lifestyle Kirk has made a career out of putting a stop to when it comes to others!) Shatner throws himself into the part (and he and guest star Sabrina Scharf throw themselves at each other) for his planet-based scenes that benefit immensely from some of Star Trek's most gorgeous location shooting, with Los Angeles's Franklin Reservoir (the fishing hole in the opening credits of the Andy Griffith show) and a specially constructed obelisk prominently featured. (Sadly, due to budget cuts this is the only location work for the season, apart from a short scene in "All Our Yesterdays"). Scharf, playing Miramanee, gives her part a nice blend of ignorance and intelligence that compliments the amnesiac Kirk, but the writers don't give her much to work with, content to let her be a simplified version of Pocahontas. (It doesn't help that she's surrounded by other Native American stereotypes, with 75 year old Richard Hale as the High Chief and 33 year old character actor Rudy Salari as the Medicine Man, both there simply to give Kirk an ally and an enemy).
On board the ship, the others get a B story, with Spock in command and the crew forced to abandon the captain to save Kirk and the inhabitants of the planet from an asteroid rushing in to collide with the planet. (It's curious that after a whole season of getting beat over the head with the prime directive, it's suddenly absent here, though it would return in TNG. Picard would just let the asteroid slam into the planet and take it out... unless Data had a pen pal there). This part of the story gives Nimoy and Kelley a chance to resurrect their bickersons relationship (which later comes to a head in "The Tholian Web") while Jimmy Doohan is busy shouting orders to imaginary engineers just offscreen because the budget doesn't allow for more than one extra. It's pretty rudimentary Star Trek, but Spock and McCoy working out a problem in their own way is always fun, and the shots of the Enterprise chasing and being chased by the asteroid are a fun back and forth bit to contrast with the surface of the planet. (Meanwhile, Composer Gerald Fried reprises his lonely Vulcan bass theme from "Amok Time" for Spock and contrasts it with high strings for Kirk to effectively transition from one deep in troubled thought to one at peace with the world).
Does "The Paradise Syndrome" approach the heights of "The Inner Light"? Not by a long shot. Kirk's life on the planet lacks the scope and depth of Picard's adventure, and the writing and guest stars aren't on the same level. But with the big three driving the plot, and the producer supplementing them with location work, special effects, and a great score, "Syndrome" offers much more entertainment than the similar but inferior offerings, "The Apple" and "A Private Little War".
Remastered version: This is a case where the original's effects are quite good, with the show reusing the planet from "Operation: Annihilate!" and creating some new, nifty asteroid shots. But CBS Digital does a fine job too, replacing the planet sphere with a better looking Earth-like world and creating all new Enterprise and asteroid effects. Originally, CBS Digital messed up a an upgraded beam that comes out of the obelisk, with the team making it red when the dialogue indicates it should be blue; but this is corrected in the Blu-ray set.