This already happens in some cases. PLoS One, for example, publishes open-access entirely online and invites community criticism:

http://www.plosone.org/static/information.action

(Sorry, I've yet to figure out how to link things and suchlike; can HTML be used here?)

One issue with just allowing anyone to comment on a paper though is a high proportion of misinformed or ignorant people who can hijack the discussion. LW gets round this very well with its judicious gardening, and other sites do this too, so perhaps it's not as big an issue as I'm making it out to be. Unmoderated comment forums tend to turn into slimepits though.