From the second scene of the Star Trek VI: The Undiscovered Country, it's clear director Meyer is going to be somewhat merciless in how he presents the film. It's not just a story about a sea change in the franchise's mythology or about the familiar cast members retiring, it's also about it being the final Star Trek movie.
Meyer gets phenomenal performances out of his cast; there's the light stuff, usually with DeForest Kelley or Walter Koenig, but he also goes dark with William Shatner and Leonard Nimoy. Somehow, Meyer manages to balance the film between serious–it's about violent bigotry, after all–and a dark gray genial. The film opens with space disaster followed with a jolting dose of that bigotry.
Playing a new crew member, Kim Cattrall gets the most comedic relief moments. Not as the target of them, but as the perpetrator. Meyer relies on her to be the audience's entry into some of the picture; she's the regular person among the titans. It's a nice narrative trick and one of the more successful ones. There are some less successful ones, which mostly get by due to the abilities of the actors. The big example is Shatner's character arc. It doesn't work because Shatner can't play it bigoted enough; Meyer tries to edit around it but still. Also less successful is Christopher Plummer's character. Plummer's great, but the part's too thin.
At the same time, lots of subtle narrative moves work out great.
The film's problematic, but incredibly successful.