I'm all for collaboration and sharing, but please be aware that you might be breaching specific laws in your country and you may be inadvertently dragging the lab (unit, group, Department) into a complicated situation.
I've found this site helpful: http://www.howcanishareit.com/. It provides advice about sharing permissions and options based on DOI.
To answer your question, my group uses EndNote Web for this, mainly because the university has a corporate subscription to the software. One of the post-grads curates the database and undergraduate students are assigned to summarising the paper, with comments provided by one PhD, one post-doc or one academic staff member. We circulate a condensed summary every week. It took a while to set up, but it now works rather smoothly.
Good luck.
PS. I just remembered that one of the post-docs presented Mendeley as an alternative, too. If we hadn't already had access to EndNote through the institutional subscription, we thought that it was a great system.