TLDR; a professor kept recycling his books in to perhaps 1000s of papers with identical content. It is however not clear from the article how all these went past peer reviewed publications for decades.
Peer reviewed publications would just care the paper on review is any good, they're not archivists to go and search for similarities. In fact in most cases they barely read the work with any substantial sense of "read".
But the article mentions peers might not be getting the works either: "
Bobbie Spellman, former editor of the journal Perspectives on Psychological Science, is confident “beyond a reasonable doubt” that Sternberg was not telling the truth when he said that “all papers in Perspectives go out for peer review, including his own introductions and discussions.” Unless, as Spellman puts it, “you believe that ‘peer review’ means asking some folks to read it and then deciding whether or not to take their advice before you approve publication of it.”"
> In fact in most cases they barely read the work with any substantial sense of "read".
I would not say this applies to most cases.
I have got many papers reviewed, have done many reviews, and have got questions from people doing other reviews, and people usually put quite some effort into it. There are exceptions, but bad reviews are not the norm, and you can usually catch them when it happens and talk with the editor about it (either if you are the author or another reviewer).
Searching for similarities should indeed be part of the job, but it is not always easy, and I agree more work should be done in that aspect.
This may be different in other fields or specific journals but, please, don't generalize.