For an especially blatant example of this, consider their bizarre claim that peer review is somehow an essential part of science -- whereas in reality, as anyone with even a cursory familiarity with the history of science knows, peer review is a bureaucratic innovation that has been widely imposed only in the decades since WW2, and science had functioned perfectly well for centuries before that.

Peer review existed in some forms well before that. The major journals like the various journals of the Royal Society often had pieces vetted by the editors rather than independent referees, but the point of independent review was not uncommon. Also, if one looks at the RW article on peer review, one sees that they list some of the more serious problems with the system.

The only bit of their section on peer review that seems really problematic is this:

If an idea has not been published in a single peer review journal, it is safe to say it is not science.

Whereas in physics and math and some other areas, many results come out in preprint form well before they are formally published (and in math their are a few examples of fairly important results that exist only in preprint form). Would you object to this sentence instead saying " If an idea has not been published in a single peer review journal, it is a warning sign that the idea may not be science?"

Most of the rest of the article seems ok to me, although others of your points may be valid, especially in regard to the low status nature of most of their examples (although in many locations alt med is pretty high status, especially in the American left-wing which undermines your claim somewhat.)