Out of all the episodes of original Trek, this is one that has stuck in my mind the most, and even though a lot of the plot is mediocre, what I remember and admire about this outing is its wonderful analysis of Spock. This is also one of the few episodes where I feel the tacky low-budget nature of the effects and props really do hinder the story.
When you can ignore the silly monsters and terrible space shots of the Galileo however, what you have is a very introspective look at our first officer, contrasted against our own psyche: It's probably Spock's worst nightmare to be enclosed in an extremely small space with six humans, but as a viewer, you don't get much better intelligent character analysis. Full of characteristic dialogue and tense drama, 'The Galileo Seven' is a highly important meditation on conflict between the heart and the brain; emotion and logic. What's tragic about it though is that all this wonderful writing is stuffed inside some uninspired 'trapped on a monster planet' story. So even though there is plenty of tension and conflict both aboard the Enterprise and the Galileo, the episodes plot fails to deliver any such suspense at least until the last ten minutes.
So where does all this character conflict occur? Well a small portion is created between Kirk and the ever-so-timely commissioner Ferris. The rest -and majority- comes from the Galileo six, against Spock. Upon closer inspection, both conflicts share common ground. Both Spock and the commissioner are the machines, who follow the rules and set about the problems logically. Then we have Kirk, and the Galileo six who argue against this approach, pleading for some emotional balance. What 'The Galileo Seven' goes on to explore is that neither is inherently correct, and that both need other. This is wonderfully brought to full climax during the episode's final scenes where both stories eventually clash together in terms of both plot and of character decisions: Kirk is forced to abide by logic and as a result Spock is forced to take an emotional approach to fix the problem.
The majority of the episode however is spent analysing Spock himself, with very little of Kirk, and it's about time too. Crawford and Bar-David skilfully exploit the situation that Spock has found himself in: trapped on a planet, in command of six other officers. As has been the case in other situations where Spock has been in temporary command, his personality traits are heightened and his logic becomes ruling. Most poignantly expressing this shift in character is the scene where Boma asks Spock to lead a burial service for a deceased crew member; obviously Spock sees no logic in halting work in order to commit to an irrational ceremony. The rest of the crew witness this and become upset at Spock's obvious disregard for loss of life.
There are many more scenes where these conflicts are developed, and as the episode goes on, I for one actually found myself being sympathetic towards Spock and resenting the irrational and over-emotional behaviour of some of the humans. Indeed even though Spock is continuously accused of being cold-hearted, distant and too focused on logic, there are many cases when the exact opposite becomes apparent: when the other members gang up on Spock, mocking his leadership and disregarding his advice; and when Spock argues that they must scare the creatures away rather than kill them. Both these examples show that even we humans can be cold, through our obsession with emotion. In the end, 'The Galileo Seven' eventually shows us one thing regarding our Vulcan in command. Spock's command style makes him a very good choice for command, but ultimately it is his lack of heart and emotion that stops him for being a good leader, at least of humans. This essentially paints him in tragic shade, developing his character into one that does all he can in the ways he knows best, but one who also cannot find the right balance between his heart and mind to reach where pure logic cannot take him. This is partly why I believe the Kirk and Spock dynamic to be so interesting. These two characters work well with each other because like Good and Evil Kirk in 'The Enemy Within', both need each other in order to succeed and survive as they are. Again, the episode's final few scenes where both characters make decisions against their nature goes to show that not only do they rely on each other, but they have also learned from the other. The focus of the story however is on Spock, and in the end, he shows more of what he has learned from his Captain than he ever had before.