Science affects multiple basic sectors of society. Therefore, the findings made in science impact what takes place at a commercial level. More specifically, errors in the literature, incorrect findings, fraudulent data, poorly written scientific reports, or studies that cannot be reproduced not only serve as a burden on tax-payers' money, but they also serve to diminish public trust in science and its findings. Therefore, there is every need to fortify the validity of data that exists in the science literature, not only to build trust among peers, and to sustain that trust, but to reestablish trust in the public and private academic sectors that are witnessing a veritable battle-ground in the world of science publishing, in some ways spurred by the rapid evolution of the open access (OA) movement. Even though many science journals, traditional and OA, claim to be peer reviewed, the truth is that different levels of peer review occur, and in some cases no, insufficient, or pseudo-peer review takes place. This ultimately leads to the erosion of quality and importance of science, allowing essentially anything to become published, provided that an outlet can be found. In some cases, predatory OA journals serve this purpose, allowing papers to be published, often without any peer review or quality control. In the light of an explosion of such cases in predatory OA publishing, and in severe inefficiencies and possible bias in the peer review of even respectable science journals, as evidenced by the increasing attention given to retractions, there is an urgent need to reform the way in which authors, editors, and publishers conduct the first line of quality control, the peer review. One way to address the problem is through post-publication peer review (PPPR), an efficient complement to traditional peer-review that allows for the continuous improvement and strengthening of the quality of science publishing. PPPR may also serve as a way to renew trust in scientific findings by correcting the literature. This article explores what is broadly being said about PPPR in the literature, so as to establish awareness and a possible first-tier prototype for the sciences for which such a system is undeveloped or weak.