It's made even better when Kirk, touched beyond words, reaches out to hug Spock, for one of the only times in the filmography. Spock rebuffing him with "not in front of the Klingons" made it a Crowning Momentof Funny.
Spock: I have lost a brother.
Kirk: I lost a brother once. I was lucky enough to get him back.
McCoy: I thought men like us didn't have families.
Kirk: I was wrong.
General Korrd deserves a mention once he dresses down commander Klaa, he seems to have gotten his 'mojo' back.
Spock's pep talk beforehand could be this or a CMOA: "Damn you sir, you will try.", depending on if you focus on Spock trying to save Kirk or Spock just talking like a badass to a Klingon general.
Personally I liked watching the growing bond between Talbot and Caithlin Dar. You only see them in the background most of the time but, they are awfully cute together.
Of course the mutual bonding between three seemingly incompatible groups like the Federation, Klingons and Romulans is something Gene Roddenberry always said was unavoidable.