I'm pretty sure the answer to the question as asked is "No". At present there does not seem to exist a unique web location dedicated to discussing each individual mathematical article.
It would be technically feasible, and to my mind advantageous, to set up a "talk" page attached to each arXiv article. I have seen this suggestion on various mathematical blogs (unfortunately, I can't remember which ones, and googling doesn't turn them up; this answer, like the question, is CW, so if you know of any, please just include a link). I certainly do not know enough about web design to draft such a system, and the folks who run the arXiv do, but are horribly overworked as it is, so I doubt that they'll be writing anything anytime soon. I encourage others with massive web-fu to create some code and send it towards the arXiv administrators, but they might not even have the time to look at it. (When you are thinking about how best to set up such a site, please do keep in mind that well-working online forums tend to have fairly heavy moderation. Moderator attention is definitely not sufficient to have a well-run site, and not strictly necessary, but it helps. Since there aren't nearly enough people out there eager to moderate random columns on the arXiv, one proposal I've seen is for arXiv authors to have the option to open a talk page, with the commitment that they themselves participate and moderate.) (Another thing to think about is how to convince NSF to fully underwrite the costs at arXiv.)
Note that although most mathematics papers are available on arXiv, it is not the only database of papers. I could imagine adding a talk page to each bibliographic entry at Numdam, for example, or to each article at Web of Science.
Something like a "talk" page does exist for (almost) every (published) mathematical article, but I don't think it's what the question is after. MathSciNet and Zentralblatt include reviews of every (almost) article in their databases, written by experts. This does not accomplish the goal of "systematically provid[ing] space for the discussion of mathematics articles", but it is something.