#7: Journey to Babel
In case you forgot: The Enterprise is on a diplomatic mission, shuttling a bunch of interstellar delegates to a Federation meeting, including Sarek and Mrs. Sarek (Spock's parents). Almost immediately the mission is beset by space intrigue: one of the delegates is murdered, someone's attempted to murder Kirk, and the Enterprise is being followed by an alien vessel. On top of that, Sarek's in the middle of a parade of heart attacks and the only thing that can save him is open heart surgery and a blood transfusion from his son.
We've got a juicy mystery going on with all these space delegates, and we get some nice drama and character development for everyone's favorite half-Vulcan. The background conflict---the delegates on their way to an important vote---is a neat look into what must be the everyday functions of Starfleet and the Federation. What complicated world exists out there, beyond the Enterprise?
There are some inconsistencies, though, with how our favorite Chief Science Officer conducts himself. First Spock offers himself up as a Vulcan blood bank, then when the chips are down says he can't because of his duty? He is so adamant about staying at his post that it makes you wonder what kind of doubts he harbors about Scotty's ability (or lack thereof) to command the Enterprise.