Indeed, the main criticism of post-publication peer review is that it would remove all external differentiation between papers, leaving no way for the outsider to differentiate between what’s good and what’s bad. And here “outsider” can mean anyone from the general public, through civil servants drafting key legislation, to scientists working on closely related problems.
Proponents of post-publication peer review would say “read the paper”. And they’re right to do so. However, the extraordinary volume of papers published makes this impossible. The mega-journals PLoS One and Scientific Reports already show us what an entirely post-publication review world would look like: they publish many great papers, and many terrible ones. Knowing which ones to read often then relies on knowing the authors’ reputation — which brings us back to the kind of personality-dependent scheme that blind peer review is supposed to circumvent.
There is no good solution!