https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1420798/

Peer review might also be useful for detecting errors or fraud. At the BMJ we did several studies where we inserted major errors into papers that we then sent to many reviewers.3,4 Nobody ever spotted all of the errors. Some reviewers did not spot any, and most reviewers spotted only about a quarter. Peer review sometimes picks up fraud by chance, but generally it is not a reliable method for detecting fraud

People have a great many fantasies about peer review, and one of the most powerful is that it is a highly objective, reliable, and consistent process. I regularly received letters from authors who were upset that the BMJ rejected their paper and then published what they thought to be a much inferior paper on the same subject. Always they saw something underhand. They found it hard to accept that peer review is a subjective and, therefore, inconsistent process.

The most famous piece of evidence on bias against authors comes from a study by DP Peters and SJ Ceci.6 They took 12 studies that came from prestigious institutions that had already been published in psychology journals. They retyped the papers, made minor changes to the titles, abstracts, and introductions but changed the authors' names and institutions. They invented institutions with names like the Tri-Valley Center for Human Potential. The papers were then resubmitted to the journals that had first published them. In only three cases did the journals realize that they had already published the paper, and eight of the remaining nine were rejected—not because of lack of originality but because of poor quality.

If "peer review" cannot detect fraud, error, or wholesale plagiarism of an article already published in the same journal, why should we lend it any credence at all?

This is not the first or even the most thorough 'review' of what is called the peer review process, but it is the most accessible to the layman.