First I should state that I disagree with anonymous review for the same reasons that I disagree with an unaccountable judiciary - the negative effects on responsibility.
However, there are several problems with the theory in this essay - the most important being that the editors know who the writer or researcher is and can decide to go ahead and publish on that score no matter what the reviewers say. The editors have a strong incentive to advance novel but true theories in that it will advance the reputation of the journal.
If reviewers anonymity is abolished, how many would dare to submit a negative review, knowing that eventually their own work might be refereed by the author?
Previously, Robin Hanson pointed out that even if implementing anonymous peer review has an effect on the acceptance rate of different papers, this doesn't necessarily tell us the previous practice was biased. Yesterday, I ran across an interesting passage suggesting one way that anonymous review might actually be harmful:
(From Richard A. Posner, "Aging and Old Age")
If this hypothesis holds (and Posner admits it hasn't been tested, at least at the time of writing), then blind review may actually slow down the acceptance of theories which are radical but true. Looking up the Peter Messeri reference gave me the article "Age Differences in the Reception of New Scientific Theories: The Case of Plate Tectonics Theory". It notes:
In this light, an older scientist's acceptance of a new, radical hypothesis should tell us to give the new hypothesis extra weight. It might even be appropriate to apply a heavier "reputation weighting" on controversial theories than established ones - we'd expect the established scientist to write papers supporting the established theories, but not controversial ones. However, blind review makes this impossible. The reviewers may even mistake the established scientist as an undiscriminating free thinker, who endorses any controversial theories simply because they're unpopular. This will slow down the acceptance of hypotheses which are, in fact, correct.
A possible objection to this could be that old scientists are unlikely to change their minds, and therefore old scientists not getting enough credit for their achievements won't have much of an effect in the spread of new hypotheses. (After all, if no old scientist endorses controversial hypotheses, then it doesn't matter if those endorsements aren't properly weighted in review.) Not so. Messeri finds that science does actually progress a lot faster than "one funeral at a time" (as Max Planck put it), and old scientists are ready to adopt new theories given sufficient evidence. While the last holdouts for outdated theories do tend to be the old, their increased security also makes them the first who are willing to publicly support new theories: