While we're at it, why not make public whoever audited or referred the paper? Why does that need to be secret?
Even if someone doesn't have a PhD or work at a research institution, they should be able to publish good science. Right now, that just isn't possible. And the opposite problem is also true: if you're a big shot in your field, you'll be able to find at least one journal that will publish whatever crap you submitted, regardless of the quality.
Imagine a system like this:
1. The reviewers on your paper not only have to collaborate on a decision to accept/reject, but also write an opinion (like a https://en.wikipedia.org/wiki/Legal_opinion) about your paper, individual to themselves, after the consensus to accept/reject is reached (so some of them will likely be https://en.wikipedia.org/wiki/Dissenting_opinion s.)
2. The reviewers are each assigned a global permanent pseudonymous identifier—a UUID, basically—known only to them and some "Society for the Advancement of the Scientific Process in Academia" organization.
3. Every vote a peer-reviewer makes, and also every opinion they write about a paper, must be registered with the same academic-process org, whose job is then to collate and publish them to the Internet under the reviewer's pseudonymous identifier.
You'd be able to use such a website to both 1. audit the peer-review process for a given paper; and 2. cross-reference a given peer-reviewer's votes/opinions.
Additionally, the standards body itself could use the cross-referencing ability to normalize peer-reviewer votes, ala how the Netflix Prize recommendation systems normalized votes by a person's interpretation of the star ratings. (They'd have to ask peer-reviewers to vote with something more fine-grained than a binary pass/fail, but that'd be an easy change.)
The only thing I would worry about in such a system, is that academics might not want the negative opinions of the peer-reviewers on their paper to pop up when random other people plug the paper's DOI into Google Scholar, because a dissent on an accepted paper might unduly impact the paper's impact-factor.
Though you will also encounter single blind reviewing. I haven't encountered a truly open review process yet.
I'm sure someone will say "well, maybe the acerbicness is the problem"; perhaps so, but I welcome the rigorous honesty with which some academics willingly write.