[foldr]

>Who pays for it: the readers of the published paper, since they benefit from not having to do the peer review themselves when they just want to use the results.

I can't make sense of this. Are you suggesting that journals should pay reviewers and finance this by charging people (more) to read articles?

As for reviewers checking statistical analyses, remember that this is peer review. The reviewers, on average, are going to be just as sloppy and ignorant and careless as the authors. If a field is awash with papers with bad stats, then most reviewers (being drawn from same same pool of people) will not be competent to check a paper's stats. Andrew Gelman isn't available to review every social science paper.