There's not much to be done with the peer-review process ... it is what it is ... and it's better than a Church-review process we had before ... Darwin's works were rejected and he had to publish the material himself ...
I think the problem in the OP's article is the shear bulk of scientific papers that need to be published, these are people's graduate degrees on the line and with so many folks in college these days there has to be a place for them to get their research published ... the so-called "paper mills" ... and I don't believe a degree is granted for publishing a duplication of someone else's work ... so figure ten's of thousands of papers being published and no incentive to verify ...
In the "hard" sciences, this isn't usually a problem ... we have a step-by-step approach to advancing the science and if anyone steps in dog poo, well, everybody will know right away and quickly search and find out who ... the "soft" sciences are more in every direction at once and odorous publications tend to not be spotted as these sciences have the prevalence of that aroma ... there's still raging debate over Freud's work, whereas everybody accepts Maxwell's work ... a shit deal if I've ever heard of one ...
Among the lay population, a surprising number of people think it's illegal to publish a scientific paper unless it's true ... and that peer-review is a certification that everything in the paper is accurate and God's own truth ... and that's just not the case ... think cold fusion ... the peer-review process only verified that all the information was given in order to duplicate the experiment ... those that tried failed to duplicate the results ... and that cold fusion paper was officially withdrawn ...
The movie Jurassic Park was based on a scientific paper ... again nobody could duplicate the results and the paper was withdrawn ... didn't stop eight sequels though ...
and for the record, the movie didn't depict Jurassic dinosaurs, they were all Cretaceous species ... yet still half the world's population think we can extract dino-DNA from amber ... because we want to ...
Today, just about anyone can take out a student loan, spend two years splitting hares, and publish in a paper mill ... here's your Master's degree ... and there's absolute no work available cutting rabbits in half ... good thing we can bankrupt out from underneath student loan debt now !!! ...
A tale I read a few months ago, kinda unrelated to the OP but still fun ... a fella got his Master's degree in fluid dynamics and went to work in aerospace, hated it, wound up felling trees in the Pacific Northwest, retired on the timber company's pension plan ... just for kicks he decided to see whatever happened to that paper he published ... it had been cited hundreds of time, the effect was even named after him, a major correction factor with boundary layer friction ... imagine his shock to learn he was famous in the field, just oblivious to this fact working out in the woods ... ha ha ha ... he applied for and received his PhD for his ground-breaking work ... so a happy ending I guess ...