Court Martial is similar to The Conscience of the King in that it's not really a science-fiction story so much as a tale from another genre, in this case, the courtroom drama. To summarize, Captain Kirk is accused of a crime he didn't commit (murder) and it's up to the crew of the Enterprise to prove that he's innocent. Into the mix are thrown a prosecutor who's an old flame of Kirk's and an old country lawyer who takes on the job of defending Kirk. Kirk proves his innocence through the sort of shenanigans typical of courtroom dramas: He gets the real criminal, in this case his supposed victim, to reveal himself and then in true heroic fashion, single-handedly beats the villain into submission and saves the day. For some reason, the members of his tribunal, all capable Starfleet officers, are just fine with sitting by and letting Kirk face the dangerous psychopath alone.
Court Martial raises some questions, the foremost being just what was Kirk thinking having Lieutenant Commander Finney, the villain of the hour, on his crew? According to Court Martial, Finney was Kirk's senior in Star Fleet until Kirk narced on him for negligently endangering the ship they were serving on. Since then, Finney's career in Star Fleet has been somewhat less than spectacular, at least compared to Kirk's. Since then, he's held a grudge against the intrepid captain and his machinations in Court Martial are intended to destroy James T. Kirk. Of course, the man is clearly mad since his plan involves faking his own death so he's not only destroying Kirk's life but his own since he can't ever surface again without running the risk of proving Kirk innocent. In case we should doubt that he's more than a little touched, when we, the audience, finally see him, he's unshaven and unkempt and from the wild look in his eyes, he's clearly got the crazy.
Going back to Kirk having Finney on the Enterprise crew: If I didn't know any better, I would think he was rubbing his success in the man's face. Of course, this flies in the face of what we know about Kirk (he's not petty) but the alternative implies that he's completely oblivious when it comes to things like human emotions, which we know he's not. If it had been Spock, the half-human/half-Vulcan who is constantly bemused by human behavior, or McCoy, the trusting humanist, making the same decision, it may have been understandable. But Kirk? It's a little bit hard to swallow.
The other question raised by Court Martial is just how old is Finney's daughter, Jamie, supposed to be?!?! Judging by the apparent age of the actress who portrayed her, I would have to guess thirty. Judging from the ridiculous blue sailor outfit she was wearing, I would guess ten. I suppose the only thing to do is to split the difference and peg her age at twenty but I'm not entirely happy with this answer.
Speaking of Jamie, her behavior is a little bit odd in Court Martial. When she first confronts Kirk, she physically assaults him, which is perfectly understandable given that he's suspected of killing her father. However, after some pretty damning evidence surfaces that seems to prove Kirk's culpability in the matter beyond a shadow of a doubt, she's apologetic to the man, citing Finney's many letters home singing Kirk's praises as proof that Kirk couldn't have killed her father.
Besides Kirk's rather convenient (for the plot) lapse in judgement, Jamie Finney's ambiguous age and her rather sudden (and unreasoned) belief in Kirk's innocence, Court Martial is well worth watching. We get to see Kirk being Kirk, cocky to the point of flirting outrageously with an old girlfriend on the eve of the court martial proceedings that could potentially deep-six his Starfleet career. We get to see Spock doing what he does best, using his logic like a scalpel to dissect the plot against his friend, Kirk. And we get to see McCoy voicing both frustration at Spock's logic and exultation at the rewards it reaps. However, as I stated at the beginning of this post, Court Martial is really a courtroom drama. For a real science-fiction story, we'll have to wait until the next episode, The Return of the Archons.