This works on a number of levels; oddly, the least effective is perhaps the science-fiction. As a political whodunnit, however, it's entirely satisfactory, with historical resonances ranging from the Cuban missile crisis through Watergate to the fall of the Soviet Union. Kirk and McCoy are framed for assassinating the Klingon chancellor (David Warner - a human in the previous installment!), and they must try and escape from a prison planet, in the movie's weakest section. Much more interesting is how the rest of the crew have to find the real killers, before the potential for a human/Klingon peace treaty becomes a war instead.
There are a number of good angles, such as Kirk's anti-Klingon prejudice (they killed his son), which is treated with surprising sympathy. The jokey approach that worked for IV, but was rapidly growing old in V, is wisely discarded in favour of a straightforward ratcheting up of the tension, though mercifully we are spared a fist-fight between Shatner and Plummer. It's closer to chess as the two sides maneouver, one group trying to protect negotiations, the other trying to sabotage them - Spock in particular has a masterful eye for "tactical omission". You could relocate the film to contemporary Earth without much trouble, and it'd be just as solid, meaning that for those who don't like SF in general, and Trek in particular, it's probably the best in the series.