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.
Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.
Belief gets in the way of learning--Robert A. Heinlein
How can I possibly put a new idea into your heads, if I do not first remove your delusions?--Robert A. Heinlein
It's not what we don't know that hurts, it's what we know that ain't so--Will Rogers
If I am entitled to something, someone else is obliged to pay--Jerry Pournelle
If a religion's teachings are true, then it should have nothing to fear from science...--dwise1
"Multiculturalism" demands that the US be tolerant of everything except its own past, culture, traditions, and identity.