The New York Times has a piece on public review, even to the point of crowdsourcing, as a partial alternative to peer review for scholarly publications. The interesting bit is that at least one journal, Shakespeare Quarterly, has tested this open review process. You can view the submitted papers and discussion (including a paper providing an information-theoretic analysis of Shakespeare). The interface seems well designed and allows commenting on individual paragraphs.
There are doubtless situations where this opens the reviewing process to trolls, flamewars, or inerudite remarks. On the other hand, assuming the comments are used to help inform a final judgement by experts, there could be advantages. Reviewing a paper is sometimes like an NP search problem, to find the contributions and weaknesses. Public review could be seen as using crowdsourcing to tackle the search problem. Certain comments would be easily verifiable by an expert, even without relying on the trustworthiness of the anonymous commenter, yet would not necessarily have been noticed by any particular expert. (The same easy-verification property is one reason Wikipedia is useful even when you're looking for a reliable answer to a question.)
In computer networking research, the closest we come to a collaborative, real-time form of reviewing is Computer Communication Review which has just recently started returning reviews to authors as they are submitted, and allowing authors to comment on the reviews.
Unrelated fun ... here's Seaquence, a clever visualization of musical composition.