For me, it's mostly a question of lyrical content and variety of sounds. These are the two qualities I find most lacking in "mainstream" or pop music.
Some indie bands are doing something interesting. They're taking the catchy (addictive) qualities of pop music but using more psychedelic and varying sounds. The repetitive, electronic sound of artists such as Lady Gaga and Kesha really grate on my short attention span. Thirty seconds pass and I tire of it.
However, lack of technical talent or musicianship has never bothered me. I don't care for a lot of classical music because I still experience a singularity of sound. Sure, there's lots of instruments and the composition is complex, but the overall aesthetic content of the music can often remain unchanged (and go on for a long time!). There's a certain refinement and blending of sounds that I find superior to the one-noted quality of a lot of music, especially the electronic variety. This of coarse is subjective (disclaimer, as if we didn't know). I offer this up as an example of catchy music with varying sounds (And St. Vincent may very well be mainstream):
http://www.youtube.com/watch?v=Hw7UeOxTGuM
Notice the entrance of flutes and string instruments mid song, then the smacking sounds of saxophones (I think), then the piercing guitar solo ending in chaotic dissonance. THIS keeps my attention. Shit, her lyrics even hit on potentially sexual topics. "I spent the summer on my back" It just remains ambiguous rather than giving you a giant, lyrical sex slap.
Of coarse, this is hardly a problem confined only to pop music. If you sample many of the artists on an "indie" site such as pitchfork, you'll soon discover a large amount of bands who are just as unvarying in sound as typical mainstream music. Yet somehow this is more hip?
I think many of us have already summed it up. INTPs don't typically care about popularity of music, but content, whatever that preferred content may be. I'm in this camp, although I may be INFP (probably not).