The focus should be on reproducing studies, not on peer-review.
Of course peer review can be of assistance in selecting studies worth putting the effort and funding into reproducing, but peer-review itself is extremely corrupted as a process, but since so many peoples careers depend on it , many of them will not talk about those issues.
I used to hold the peer-review and journal process on a pedestal. Then when working at a genetics lab I ended up having to read a lot of papers to get my sysadmin work done, and started realizing just how bad so many papers are, even though published in "reputable" journals.
For example, since publishing is seen as so vital to some people, I noticed many of them would "consult" on another groups paper just to get their name on the paper, even though they did almost no work, and then those same people would turn around and say stuff like "I've been published X times!" as a sort of reinforcement of authoritativeness (and as advertisement).
People are gaming the system because hardly anyone is actually checking them. Beyond that, the actual peer-review process itself seems to be very lackluster in rigor on it own.
I think there should be a certain amount of public research funding that should be earmarked to go directly to independent reproducability labs.
On top of it all, all this research that the public is funding is often behind a fucking paywall... and that's not just bullshit, it's theft and misuse of public funds. It should be required that publicly funded research should be publicly published, and therefore available for more eyes to see and review.