From Garrett S. Christensen and Edward Miguel, from their survey of methodological problems in economic research:
Another potentially useful tool is post-publication peer review. Formalizing post-publication peer review puts us in relatively uncharted waters. Yet it is worth noting that all four of the AEA’s American Economic Journals allow for comments to appear on every article’s official webpage post-publication (anonymous comments are not allowed). The feature does not appear to be widely used, but in one case…comments placed on the website have actually resulted in changes to the article between its initial online pre-publication and the final published version.
One of the biggest problems with “economics as a science” is that economists themselves cannot usually admit how irrelevant so much of the work — even the quality work — turns out to be. I’m all for worrying about reproducibility, transparency, and the like, but sometimes I feel those micro-debates distract our attention from this bigger and broader problem and indeed help to obscure that problem.
Addendum: This website, JournalTalk, does the same thing.