Shatner reciting the "We The People" is one of my favourite things of all Trek. Its just such a gloriously over the top performance, but also has a raw power behind it I find alluring. The message that these important words could have their meaning and intent distorted or outright forgotten over centuries or milennia feels astonishly relevant in the politically partisan 21st century, where the foundation stones of American society are constantly debated and interpreted by people who could not possibly have understood or known the intent of those founders. It takes a Canadian actor to point this out, of course.
I also love the concept of Captain Ron Tracey. He's the proof in the pudding that, in Kirk's time at least, humans are not so 'evolved' as to be beyond greed and other such things. He punctures the utopian myth, and brings Star Trek back into the realm of how real people really act. Also, another really powerful reflection of Kirk: here is another great and glorious Starfleet Captain, a Captain of a constitution class vessel no less, potentially Kirk's equal in literally every way, but corrupted, and Kirk's disappointment at that is profound. Them fighting it out at the end brings us back to raw humanity at its worst, a fight for survival.
I really love "The Omega Glory".