I believe that some major flaws in the peer-review process are involved with anonymity. I believe our current review process opens up areas for abuse in the part of the reviewers in two main ways:
A) By knowing who the authors of a study are, the reviewers can be biased. especially if the authors are in direct competition with the reviewer's lab. Also, knowing the identity of the authors can make it harder for first time grad-students to get their work published as these people may be unfairly targeted as inexperienced based not on the merits of their science (and the models they propose) but based on their scientific status.
B) By remaining anonymous these reviewers can be far more critical to one's work without necessarily being constructive as they do not have to fear criticism from the wider scientific community for being, perhaps, too one-sided/biased.
I believe that a fair review process would be one that fosters diplomacy at all levels. This can be accomplished by either allowing both the authors of a study and the reviewers to be anonymous so that a review can focus solely on the science, or by eliminating the anonymity status from the reviewers so that the authors and the scientific community know who is reviewing what, which would prevent unfair and biased reviews.