The only real downside I see is that it allows the authors to contact and potentially bias the reviewer to affect a potential review of the written material.
This must vary across disciplines. While in your field the pool of reviewers might be public, in my own field most journals keep confidential their set of preferred people to turn to for reviews.
Sometimes you can take a pretty good guess who it is based on the topic and the references (e.g., citations to in-press papers on obscure topics is usually a give away). Other times, though, it's difficult to tell who the authors are.
People often also think they know who the author and/or reviewers are when they are really totally wrong. I've reviewed papers and seen other reviewers cite my papers in a way that I thought "damn, that looks like something I'd write" when it was not. Similarly, I've seen reviewers think they know who the author is when they're completely off.
I personally think anonymous reviews are critical, because it keeps some modicum of shielding of reviewers against retribution for negative comments. It's not 100% anonymous of course, but it's anonymous enough to create enough doubt about who the reviewers and authors actually are.
v1 will be a search + reading interface for scientific articles with p2p datasources (provided as hyperdrive feeds [2]). v2 will have arbitrary features that can be used to customise the reading experience, such as marking retractions/update/expressions of concern, connecting post-publication peer reviews to articles, etc.
we're at #dat and #sciencefair on freenode, would love to talk