"No, peer review is no criterion for deciding whether something that someone is saying is scientifically meaningful. The criterion for deciding whether someone is saying something scientifically meaningful is nothing more nor less than whether he or she >is< saying something scientifically meaningful. Peer review may sometimes be helpful is getting your work accepted, but this is not the same thing as producing scientifically meaningful work."
Well, this seems a bit circular, because the criterion you're using to evaluate "scientifically meaningful" is also your definition. In other words, we know it because we know it.
Peer review is less about getting work accepted than about evaluating whether or not the person(s) writing the article are following the scientific method in their approach. Do they propose a testable hypothesis? Is their work open to others who can test it or at least observe what they did (i.e., repeatability)? Is the work up-to-date with current systematic hypotheses, and does it address these? Can the hypothesis be falsified? If there are statistical data, are these presented in such a way that others can repeat the tests? As science is by definition a narrow discipline that seeks to pose answerable questions about the physical universe, have the author(s) of the article stepped beyond the bounds of scientific inquiry? And so forth.
In essence, peer review is part of the publication process wherein other scientists evaluate the article for evidence that the author(s) followed the scientific method. Scientifically meaningful articles have hypotheses, theories, etc., or statements that can be tested, falsified, and observed/tested repeatedly by other researchers. Your scientific peers, scientists who are involved in similar research and understand its limitations, are usually the "best" people to review your submitted articles because they deal with similar "protocols."
When you submit an article to peer review, you are saying, "I might be wrong, have overlooked something, and I could use additional input. What do you, my scientific peers, think? Have I misled myself, etc.?" This is ultimately the value of peer review, because none of us is unbiased. If several people can look at your reported results, observations, etc., and draw similar conclusions, this strengthens your article and its contribution to the scientific process.
Therefore, peer review IS a great criterion for evaluating the scientific importance and/or value of the article. This is why we trust the results of peer reviewed medical journal over the claims of someone on TV at 2:00am saying his/her clinical studies prove shark cartilage cures cancer and ends insomnia. As usual, peer review, like any human endeavor, can be corrupted, but in general it is the best way we know to dull the influence of personal bias on reported research results.
Anyone care to peer review me? =)