Obviously the concept of 'good' music is totally subjective, but there are a few factors that people commonly cite along with an artist generally considered to get high marks for it:
Technical Skill is almost a non-factor in pop music today, and modern technology reduces the importance of even knowing how to play an instrument anyway.
Production quality on the other hand is critical. Modern pop music is considered by many to be overproduced, but the fact is that underproduced music simply won't sell.
Grooviness and originality are critical factors which are not so easily analyzed. By grooviness, I mean the general appeal or 'catchiness' of the music to a mass audience. Although some popular music is very original, music that consistently makes the Billboard Charts seems to usually follow the formula of the day.
I view the popularity of music as a bell curve. On the leading edge you have the less-popular, very experimental and original music of which music snobs are notorious for liking. On the trailing edge you have played out music which happens after a big music fad hits and all of a sudden everybody wants to play that kind of music (but are too late). In the middle, you have whatever is playing on MTV right now.
Well duh, but what's the significance of that? My own theory is that the human ear in general is tuned to things it recognizes. For music to be considered good it must appeal to something the listener already knows. People say that want something original, but if it doesn't have influences from past music they recognize, they won't like it. It will just sound like random noise. At the same time, people get sick of hearing the same old stuff.
For a contemporary band to be considered 'good' requires a delicate balance between musical creativity and a firm grounding in established tradition. Of course, there are those musicians who only care about their creative vision, and not the appeal of the final product. Many of these musicians go on to be recognized as geniuses once their music has enough time to absorb into society (ie. once the word spreads and new musicians become influenced by it).
Wick suggests that my use of Grooviness actually reflects two ideas: Persistence of Vision (meaning capturing the essence of the sound in a focused manner) and Catchiness. It is an interesting thought, but I maintain that Persistance of Vision is something that only a music expert can judge whereas the general concept of Grooviness I layed out is something most people use regularly. Persistence of Vision is quite important to the quality of music, but I don't think it's necessary in the discussion of popular music (or at least, I'm not qualified to say much about it since I am not trained in Music Theory).