I do think a bigger budget would have made TUC better in terms of a larger sense of scale. Bigger sets, new model ships, fleets instead of single ships, higher quality film in the cameras...
You are right about the cold war parallel, of course, but there were also some overt references to racism:
- Chekov's line "Guess who's coming to dinner?" is a reference to a 1960s film about a black man coming to dinner with a white family.
- The Klingon woman has the line " 'Human rights.' Why, the very name is racist. The Federation is no more than a 'homo sapiens' only club."
- A nameless Enterprise crewman says of Klingons "What about that smell? You know only the top-of-the-line models can even talk..."
- Uhura says "Did you see the way they ate?", and later admits "I felt like Lieutenant Valeris", i.e. prejudiced against Klingons.
Thing is, each instance of what you're calling overt racism can be traced back to middle America's reaction to the Soviets, and their reaction right back at us.
For instance, Soviet bloc athletes at the Olympics were routinely called machines, robots, etc., which falls directly in line with the "top of the line models" line. Complaining about table manners can be compared directly to our interpretation of certain social mores they exhibited(and still do today, at that). Azetbur's complaint about the 'homo sapiens only club' correlates with how Soviet citizens interpreted how they were characterized and treated in the U.S. I remember in high school in the early '80s it being said "there are more teachers of English in the Soviet Union than there are students of Russian in the U.S." This wasn't far off. And very little of it is actually related to race, so much as it is fear and loathing of the 'other'. We just interpret it that way in hindsight.