Sometimes it feels obvious to me. I can read a page of a novel and realize "Huh, this writing feels clunky." Other times, I'll look at a painting that seems like gibberish to me, and which is presented without any explanation that helps me appreciate it.
Still other times, I will love a musical artist and consider them to have depth and subtlety, but a close friend will completely dismiss their music as nonsense. As a music school graduate and someone who can use music theory to "prove" for myself that the music I like is better than the music they like, I feel satisfied that I'm right; but of course, the friends also don't understand or really care about music theory, and are equally convinced that their own taste is correct.
How do you decide for yourself whether it's a quality problem or a problem with the consumer of the art? Have you had revelatory experiences where friends successfully got you to see the beauty in something you'd previously thought was crap?
For instance, it becomes hairy once you get down to make any sort of meaningful comparison between the quality of musicians you like, even if the criteria are pretty meaningful. Is Chopin better than Katy Perry because his works are harmonically richer? Bach because of superior use of counterpoint? Maybe Ivan Wyshnegradsky for his use of non-standard tuning systems?
Something is good if you are able to appreciate and enjoy it. Trying to justify why you like/dislike something is not going to be very fruitful in thr grand scheme of things, unless you just want to find similar things that you'd enjoy.
At the end, he didn't think he got much out of it.
Then he went to a museum with Western Art. And found it a bit odd. He had grown used to the Asian styles and motifs.
Another story I have comes from a friend of mine. His (British) parents had a very odd cartoon book. It contained cartoons of people on fox hunts. They were actually political cartoons, and to understand them you had to know how mid-20th century British MPs were caricatured. He didn't, so it make no sense to him.
Duchamp's Fountain is something which is hard to understood without knowledge of art history - if only because that transgressiveness is now much more common because of Duchamp.
Someone deeply into classical Western music might have no interest in classical Indian ragas. Indeed, the music theory you learned doesn't describe ragas.
Innumerable art museum visitors have looked at something piece of art and exclaimed "my 4 year old can do better than that!"
And so on. For all styles of art.
That said, to get to your questions:
1) "How do you decide for yourself whether it's a quality problem or a problem with the consumer of the art?"
It's always a problem with the consumer. I may grow to admire the art of 4 year olds. I may find a pile tossed coffee grounds to be the next masterpiece.
But is it my problem that I don't care to put in that effort? No. Unless I want it to be.
2) "...something you'd previously thought was crap?"
I'm struggling to think of things which fit that description. Most things I file under "I don't know how to appreciate it."
Perhaps a good example is the false and snobbish belief I had that I was too mature to read, watch, and enjoy children's literature and shows. I remember dismissing Fraggle Rock because "that's for kids". I then watched it when I was 30-something and kicked myself for my earlier viewpoints.
In college I looked a bit down on a friend who enjoyed reading children's literature. Now that I have kids, I can say there's some really great stories out there - stories that don't require a kid in order to enjoy them.
The thing about communication of this sort is that its error-prone: the "message" you receive may not be (and often is not) the "message" the artist was intending to convey. If the artist's communication style doesn't match your own way of thinking well enough, you may not get a message at all.
When that happens, that's not your fault. Nor is it the artist's. It's just a case of two people not connecting.