Peer review has been used for regulation of scientific knowledge for almost 350 years. Were there any common mechanisms for verification and regulation of scientific knowledge before peer review became widespread? Are there any other methods of verification of scientific knowledge commonly used now?
Before 350 years ago, published academic works derived from lectures, repetitions, or disputations (source):
In all the faculties the work of teaching centred about books, i.e. the texts, compilations, and glosses which were regarded as the chief authorities in each subject. At the beginning of the year (or semester) the books were distributed among the professors, who were obliged to use them in accordance with the regulations established by each faculty regarding the daily schedule, the length of the course, the hall to be used, the academic dress to be worn, and the method to be followed. The lecture was in the strict sense a praelectio (whence the German Vorlesung); the professor had to read the text; in the ordinary lectures, he was not allowed to dictate anything beyond the divisions and conclusions and such corrections of the text as he deemed necessary. The scholars were supposed to have their own copies of the text; if they were too poor to procure the books, the professor might dictate the text to them, not in the regular lecture but at special classes or exercises (repetitions). The plan of the lecture was analytic: careful explanation and definition of terms (ponere et determinare); division of the matter and discussion of the several points followed by a summary of the essential (scindere et summare); presentation of problems suggested by the text (quaestiones), and solution of objections. In lectures on law the reading of the glosses was an important feature, and cases were frequently proposed to illustrate principles. At the ordinary lectures, the scholars were not supposed to ask questions; at the extraordinary, greater freedom was permitted, the scholars being encouraged to express their doubts as to the meaning of the texts and to request further information on obscure matters. More thorough training, however, was given in the resumption and repetitions which the masters held at stated times for the treatment of special problems. The exercises, conducted in dialectical form, afforded full opportunity for discussion between scholar and master; and they served as examinations by which the progress of the scholar was tested. But the most important of the academic exercises was the disputation. This was of two kinds: d. ordinaria and d. de quodlibet. The ordinary disputation took place every week and lasted from morning till noon, or till evening according to the number of participants. On the day set apart for this purposes the lectures and other exercises were suspended, so that all the masters, bachelors, and scholars might be present at the disputation. One of the masters (disputans) announced, in the form of question or thesis, the subject of the debate; other masters (opponentes) presented arguments against the thesis; answers to the arguments were given by two or three bachelors (respondentes) appointed for the occasion. The number of arguments were fixed by statute or was fixed by the dean of the faculty whose duty it was to preside. Throughout the disputation the syllogistic form was employed. The disputation de quodlibet was held only once a year, but with greater solemnity than the ordinary, and over a wider range of topics. The master elected or appointed for the occasion, and known as the quodlibetarius, had to debate a separate question with each of the other masters who chose to enter the lists. The disputation lasted several days, sometimes a fortnight. The arguments and their solutions were written out and preserved in book form. A specimen may be found in the "Quodlibetales" of St. Thomas. It was mainly out of these lectures, repetitions, and disputations that the works of the medieval doctors grew; so that the various commentaries, summae, and books of "sentences" afford the best idea of university teaching both as to content and as to method.
Disputations could be thought of as a public, open, oral form of peer review because they laid out all the arguments for and against a particular thesis, distilling out the truth.
Also, European universities were under the control of the Catholic Church, which had ultimate say what was taught at the universities, what textbooks could be used, etc. See, e.g., the Condemnations of 1277, which liberated the universities from intransigent Aristotelianism.
Scholasticism heavily relied on the critical reading of (and rigorous debate about) existing texts.
It emphasized authority rather than individual research, but the important thing that was lacking was experimentation as the ultimate arbiter of research.
And I think that is something that even today is often overlooked (if not outright neglected) in the peer review process of natural sciences: if you've read through a paper and thoroughly analyzed the autors' methods and reasoning, you may have ensured that certain kinds of errors and dishonesty are not present, but you still haven't actually verified anything until you've replicated their experimental results!