This planet-based Vietnam War allegory by Don Ingalls (an old friend of Gene Roddenberry's credited under a pseudonym) is a simplified version of how some Americans viewed the Vietnam conflict in the late 1960s. (In a way, it's interesting to see what the writer comes up with considering he doesn't know how the real war - which is even referenced in the dialogue - will end. That said, with what we know now, the episode's story is not a very good representation of what was really going on).
With the the war, an old friend of Kirk's, the Klingons, a mysterious woman, a wild animal, and a B story with Spock on the ship, the episode probably has too many elements; it's like a redo of "Friday's Child" with more complexity. The interesting (and most unique) about the Spock story is that it's really a brief comedy runner that clears the deck for the main thrust of the episode to be a straight up Kirk/McCoy story. As great as Nimoy is, Kelley is his equal, and the episode benefits from leaning on his talent and exploring the always interesting Kirk/McCoy relationship. That said, even Kelley has difficulty carrying the episode when the writer uses this opportunity to employ parallel scenes where Kirk and Spock (on the planet and aboard the ship) struggle to regain consciousness. It's something that probably looked cute on paper, but it basically turns one quarter of the episode over to Kelley and the guest stars, and only one of those actors is decent. (I'll leave it to you to guess which). The most notable guest appearance is that of Nancy Kovak, who plays Nona, a shaman of sorts and the focal point of the story. It doesn't take long before the episode establishes two notable aspects to the character: A, she knows her husband's a tool, B, she gets really annoying really quickly.
A planet-based episode that mixes location shooting with stage sets, the setting is actually quite well done, and somewhere in the concept is an interesting story. (The step by step progression of Nona's husband losing his innocence would be a more interesting focal point). Unfortunately, the pieces don't come together, and the result is a bit of a mess. (First season's "Errand of Mercy" does a similar concept better).
Remastered Version: "Private Little War" gets a basic upgrade with new shots of the Enterprise and a more realistic, Earth-like planet replacing the original's reuse of the "Friday's Child" globe.