It raises questions around using peer-review as a mark of scientific quality. If it is, why does peer reviewed science time and time again turn out to have enormous glaring quality problems?
In fact, peer review is often more about novelty and importance rather than rigor. Very well structured research will get rejected if it isn't seen as contributing to the field in a nontrivial way.
A few fields (psych is the big one) are funding replication grants. That'd be the true mark of quality.
This is actually deeply problematic, as a part of what's driving the replication problems is specifically publication bias. If the only thing that gets published are unexpected or noteworthy results, you're selecting for statistical aberrations.
Peer review is not infallible, neither is it a mark of scientific quality, as you say. I appreciate that people tend to use it like that- you read, in articles in the lay press, that such-and-such study was "not published in a peer-reviewed journal" as if to say that we can't be sure of the quality of the study and that, conversely, if it was peer-reviewed, we could. That's not right. Peer review is not a sufficient condition to guarantee correct results. It's not even a necessary condition. Like I say in my comment above it is one mechanism of modern research practices that helps improve the quality of published papers.
Wrong, sorry. Disclaimer: I'm not a homeopath and don't go to any. Most of them are, in fact, quacks.
There are, unfortunately, chronic diseases which can be treated but not cured. Mainstream doctors and Big Pharma make a living off of those. If you have one of those, "well, why NOT try a homeopath?" is a perfectly rationale response.
"Sinus rinsing" is something that might be termed "homeopathy." It IS medically respectable, unlike most of their "treatments" (like magnets).
Is that a failure of peer-review though? Or is it more of a consequence that even if you do everything right you'll still get some false positives some of the time, and negative results tend not to get published at all?
(i.e. the problem that pre-registration for medical trials hopes to solve - https://en.wikipedia.org/wiki/Preregistration_(science) )