there are tons of potential pitfalls and a combination of
experimental limitations
you provided some, which are at least partially addressed by the study design. (I don't think it's your point, but let me agree that "the scientist can cheat" is always true).
poor academic incentives,
this is addressed because it is double-blind
insufficient statistical and scientific training
this is (partially) addressed by peer review, and the availability of the data. you can't make this general criticism of the paper at hand: find the place where the design or statistics used were in error.
I think it’s bad science, that will one day
retrospectively be viewed as invalid scientific method.
that's a claim without any evidence to back it p.
I think the way to combat this is to avoid studies
that solely attempt to demonstrate an effect, but to
complement that part of an investigation with additional
studies that demonstrate a plausible explanation. This
reduces the risk of false positives and increases our
confidence in the result.
If you have a double-blind, placebo-controlled, randomized clinical trial then what can the mechanism possibly add? Is an effective medication less effective because we don't understand how it works? If you want an amazing example, read about the mechanism of action of general anesthesia: we have many ideas about how it works, but nobody really knows. Nobody gets caught up by this when their appendix ruptures. I hope, for your sake, that you will lower your standards in the event that you need surgery.
The additional studies could take the form (for example)
of deliberately intervening such that the effect should
be manipulated by the intervention in a predictable and
measurable way. Essentially, come at the hypothesis “from
another angle”.
If you have a properly designed and executed randomized, double blind, placebo controlled trial, then you have measured the effect of the intervention, and only the intervention. You can repeat it in order to gain confidence, but you have to decide when the diminishing returns of "more confidence" are not worth your study dollar. And for curcurmin, which is cheap and has low side effects... it's probably not that far away.
edit: fixed formatting