The peer review system in science, whereby prior to publication manuscripts are reviewed by anonymous peers, has come under recent criticism in a debate at the Royal Society, at which a case for its abolition was argued.
The concept that a piece of research should not be reviewed by other experts in the field is, of course, ridiculous. But I think doing away with peer review in its present form is feasible. I wrote about this in 2012, and reproduce what my ideas would be here, with some tweaks.
There are two major current problems: the cost of publishing and access, and the inequities of the peer review process. Both could be cured at once.
We need ONLY ONE, publicly-run, open-access scientific publishing domain to which ALL ARTICLES are uploaded for free, in whatever format wished for by the authors and without prior peer review. This domain would subsume all existing primary research publishing. After an initial, publically-funded development phase, the small costs of maintaining this domain could be obtained through discreet advertising revenues. The model thus obviates both the need for charging huge amounts for access to journals and the need to charge authors for each publication submitted.
Once an article is uploaded it will easily be able to be found by a keyword search, such as exists in PubMed or Web of Science. Reviewing would not be solicited but would be open and online, in the fashion of "comments" to a blog entry. Any given article might thus receive many or no reviews. PubPeer goes a step in this direction. However, in my opinion no reviews would be anonymous: only registered reviewers who have revealed their identities would be allowed to post comments.
Before entering comments, the qualifications of the commenter would be verified e.g. PhD in the field of the article. All may comment, even the unqualified, but their qualifications would be public. I would suggest separate comment threads for specialists and non-specialists. Many of the reviews, even from the specialists, are likely to be incompetent, but the reviews would also be open to review, and ranking, as would the reviews of the reviews etc.. The paper itself would be continuously modifiable by the authors (as in Wikipedia), to add results or respond to criticisms etc.
In the above system there would be no need for a decision to be made a priori as to whether an article is "of sufficient general interest" before publication - this would all be decided by the readers afterwards: a points system could be devised whereby an article gains prominence depending on how many times it is accessed from different computers, cited later on, and on the reviews received. As an article rises in points, so would its visibility in the web domain. Extremely hot articles would be expected to very rapidly gain prominence.