A 1983 Webster's Collegiate gives the definition of problematic as "1: a. difficult to settle or decide b. not definite or settled c. open to question or debate 2: expressing or supporting a possibility".
(Bold type, proffered synonyms, and examples omitted.)
The sense of "problematic" as in "you've got a problem" developed after 1968, perhaps after 1990.
So if I go back and reread the quote that I had posted, is the critique that the public's tastes are not fixed, and change across geography and time? I'm still not sure what he was really getting at, I guess.
This sentence scores as 'extremely difficult' or 'difficult' on most readability scores, and it's just unnecessarily flowery.
Basically, I think the point is that the idea of the 'taste of the public' is just a shorthand for 'something that appeals to lots of people with differing tastes'.
The author's key point (I think) is that 'engineering' music somehow makes it less artistic, and the 'problematic taste of the public' is a tangent which explores why sound engineers do what they do, rather than being part of the main argument.
It was written for the Paris Review subscribers of 1968. I imagine that they found little difficulty in understanding it.
Regardless, I think you're right, the target audience of this as it's written probably would not have issues understanding it.