I've been on both sides of peer review.
I think the issue is different among the different fields of science. Some, such as cancer research mentioned above, are critical. Others, such as sociology, matter hardly at all.
Anonymous reviews let reviewers say what they really think, but they also shield shills who might have a vested interest, or an axe to grind.
Also, an editor can send an article to any of a number of reviewers and by careful selection can probably get the results he is looking for.
The open review is a good idea, as that lets a larger number of reviewers get their say. But that's essentially what the publishing part of science does anyway.
What Coyote describes is the process for most of the basic science research in the field of biology.
What you need is good editors. They are the linch pin of the entire process. Reviewers are there to help the editor, to find mistakes that the editor may not necessarily be able to catch. Also, reviewers will have the specialized knowledge of the important and current findings within that narrow field of research.
In the end, it is the editor that makes the decision to publish a paper or not. The strength of any journal is based on how well the editors do their job. It is the job of an editor to find the best reviewers that will give the most honest reviews. That means finding reviewers who have limited conflicts of interest and can look past disagreements in order to see the quality of the science itself.
As of now, anonymity increases the quality of reviews. The system is working well where the reviewers are accountable to the editor. In the end, if reviewers try to take out the competition for grants by blocking publications, then their publications will be blocked as well. The editor plays the role of the referee so that there is fair play.
Edited by Taq, : No reason given.