We just pushed an update to webcompat.com today that will allow you to view issues inside of the site. For example, check out this issue reported about a problem for IE 11 users on the toyota.com site.
For now this is a READONLY update, but one of the next updates to tackle is to allow (logged in) users to add comments, labels, and do the other kinds of issue-y interaction things one does with GitHub issues. For now there's a link to each issue on GitHub at the bottom of the page if you want to add a comment (which is either super lame, or an advanced agile iteration hack).
If you'd like to get involved hacking on webcompat.com, drop by #webcompat on Mozilla's IRC network or dive into one of our open issues. And naturally since I'm involved, there's probably tons of bugs that deserve reports and patches.