Publication of review's comments on scientific papers?
It would probably harm the reviewing process itself as it stands at the moment. Many reviewers only agree to review, because they can be anonymous and their comments are confidential. I therefore do not believe, that any editor of a traditional journal would give you access to the reviewer comments on a paper, however you ask.

Having said that, there are some recent developments in some journals, which I appreciate a lot, and which go in that direction:


Copernicus Publications is promoting an open review process. All manuscripts are published in a discussions version (pre-review), and reviewer comments are published and archived together with the article (and can always be referred to from the finally published paper).
Frontiers is promoting non-anaonymous reviews. The reviewers are mentioned by name on the title page of each article. In my opinion, this increases the quality and objectivity of reviews a lot.
There is always the possibility to publish additional reviews after publication on post-publication peer review sites, like PubPeer. Those can help you to find errors in already published articles, which may have evaded the original manuscript reviewers.