The current system of scientific publishing is clearly outdated.
There are issues with the biases, but also with for-profit nature of the system that charges huge sums of money for accessing the work of researchers funded by public grants and reviewed by researchers for free, financed by public money.
Then add to this all those phony journals, that are theoretically peer reviewed, but have very low (or non-existent) standards and accept everything to make money or simply exist because some big-pharma company uses them to publish skewed tests to get FDA approvals, etc.
I think one or two additional special-purpose journals would not really change the landscape.
IMO, what we need is a complete modern infrastructure based on state of the art IT/social networking. One that allows the review of articles even after they officially appeared with an elaborate voting system that factors in the credibility of the reviewers, It should make it possible to add (publish) refutations and the publication of positive or negative attempts of replications, etc and organize the articles with their support/refutations/endorsements in an easily accessible database.
Ideally, such a system could work both as a rating and publication medium, but with the current scientific publishing lobby, it would not have much chance to take off. The only chance is to do this by extending an existing meta-system (e.g. citeseer) with a general discussion/rating/publishing forum, that would allow the publication of critics/refusals/extensions of existing papers maybe even in a peer-reviewed manner.
In the field that I work, I see that the scientific community discusses and generally supports such changes and given all the efforts and progress of the last decade I'd be surprised if we won't see such (or similar) one or more systems emerging in the next 10 years.
Yes, that would be better, but as yourself note, it's a big change that's unlikely to happen in one go. On the other hand, specialized journals are not a novelty, and considering that at least some folks took that specific specialization up, it appears to be more an issue of advertising than invention.
But nobody said this problem should be attacked on just one front. More (different) attempts mean more chances of success, no?
One of Seed Magazine's "Revolutionary Minds" is Moshe Pritsker, who created the Journal of Visualized Experiments, which to me looks like a very cool idea. I imagine that early on it may have looked somewhat silly ("he can't implant engineered tissue in a rat heart and he calls himself a scientist?!"), so it's nice to know JoVE is picking up pace.
Many folks keep pointing out how published research is itself biased towards positive results, and how replication (and failed replication!) trumps mere "first!!!11" publication. If regular journals don't have good incentives to publish "mere" (failed) replication studies, why not create a journal that would be dedicated entirely to them? I can't speak about the logistics, but I imagine it can be anything from a start-up (a la JoVE) to an open depository (a la arxiv.org).
I am not part of academia, but I understand that there are a few folks here who are. What do you say?
[EDIT: Andrew Kemendo notes two such journals in the comments: http://www.jnrbm.com/ and http://www.jnr-eeb.org/index.php/jnr.]