My one publication through the traditional system went through a rigorous peer review which actually included two anonymous reviewers instead of the traditional one. It has a correct mathematical argument by the established standards of its time. But its conclusion is incorrect!
The paper is "Advanced Polynomial Factorization", published in the Southwest Journal of Pure and Applied Mathematics, Issue 2, December 2003, pp. 6–8.
Here's the link to the original paper in Postscript format:
The argument given is correct by established mathematical standards, but appears to establish a wrong conclusion.
Can you find an error?
Turns out there is none under established mathematical understanding, but the conclusion is, nonetheless, provably incorrect with that same established mathematics. Contradiction!!!
The journal bravely I think published the paper, but then less so tried to remove it after publication!
The journal itself shut down not too long after.
Thankfully it has remained publicly available through EMIS, which also chose to keep my paper available despite the attempt by the journal's chief editor to withdraw it, and I am deeply grateful to them for so doing.
And here I think anonymous peer review clearly worked and I want to thank the reviewers. I also wish to thank the editors, and given the enormity of this paper, and what it demonstrates, I can understand how they might have shrank back later.
The result is as big as other work on completeness and I myself have taken the time to thoughtfully consider it for years until I felt I had it clearly resolved.
The issue is as huge for completeness as other work in this area, as it raises the question of, how do we really know what's true?
Interested parties should try to find an error, did the reviewers miss anything?