Galileo Seven is probably one of the more recognized Star Trek episodes in my opinion. This is due to a variety of reasons: Spock's First command is a giant failure (he loses two crewmen by his own bad decision making) and after his Vulcan logic fails Spock resorts to human emotions throughout the episode.
The Enterprise is set to deliver vaccines to Marcus 3 but for whatever reason make a pit stop (my first Amazing Race reference lol) at Murasaki 12. In hindsight this might have been Kirk's fault for letting Spock and others go but Spock's handling while in first command though are a bigger disaster.
For instance when Spock and company land on the planet known as Taurus 2 they are eventually attacked by giant barbarians for a lack of a better word. The first scout Latimer is killed by a spear through the back (shown in graphic fashion which for this time on TV was very violent). Spock adhering to his "logical" form of non-violence tries to evade the barbarians seeking more to annoy them hoping them to go away. This is hilarious. Clearly if logic was a factor as the other crewman have said included the next victim ,Gaetano, then actually the next "logical" step would be to wipe out the threat.
Spock's "logic" seems to be more relied on his upbringings as a Vulcan thus portraying an adherence to a human quality- that is the human behavior to be molded by the actions of others. Other areas of Spock's irrationality is his decision to say to he will pick one of the crewman to stay behind. See the ship the Galileo is stuck in the planet with fuel gone for the most part. Spock saying he would logically pick someone to die has no logic, once again a human trait is displayed here that is desperation and a lack of hope in sacrificing someone so others can leave. No matter how many times Spock could think over this decision there be no "logical" candidate.
For me I love it because it shows Spock's human qualities something of which the writers at the beginning (with the exception of the Pilot "The Cage") was something they didn't want to pursue (even though by the last season we would see more of Spock's human emotion).
Anyhow, continuing on Spock's failure of logic and his human emotions coming out (he decides not to give one of the dead crewman a proper burial even though that would be the "logical" thing to do), it is Scotty who comes to the rescue. Fans are used to seeing Scotty make up excuses on the show like he can't get the warp engines going or something like that but it is Scotty who comes up with the plans to leave the planet by redirecting the phaser power to engines.
So that's why I love this episode. I think for those who sort of saw Spock as a hypocrite or as a guy who despite his alleged logical attributes here is the real Spock coming out in a way with his human emotions coupled with bad decision making which are a human trait. Besides that this episode had decent action scenes, story, and special effects (for the time)