People are far more likely to view music/art in a subjective sense than an objective one. Except I find people who are a bit more intelligent or well educated may view art with a bit more of an objective viewpoint than the average person. But yeah, art is more or less subjective/arbitrary. I voted for the last option.
Talent really isn't that relevant. There's tons of bands who aren't very skilled and are well-liked, and tons of bands who are quite skilled but are overlooked. Skill doesn't always translate to good songwriting or creativity and vice versa etc.
The passion and dedication of the artists isn't always apparent in the band's music. People are far likely to make assumptions about the band anyhow, whether they are accurate or not. If Darkthrone doesn't rehearse/practice their skill much so they purposely have a sloppy, raw sounding album then how much passion and dedication to their music do they have? And what about band like Dimmu Borgir, they're sellouts right? So they can't have any passion or dedication to the music they make.
I think a collective perception, or just a single person's will dictate this. There is no real way to tell.
Influence, I personally don't think is all that significant though you can easily look back in music history and argue otherwise. But typically, people will often just accept which bands are considered classics etc. Like, a good album by a highly praised band is better than fantastic album by band not considered so - this sort of ties in with popularity/commercial success a bit. And Korn was highly influencial to the "nu-metal" scene - are they a great band? It depends on how you look at things I suppose.
Popularity and commercial success really doesn't mean anything. That has more to do with how well the band is promoted, and touring - assuming they're are a good band to begin with.
Gah, I just woke up, hopefully this makes sense.