I think the bigger problem is not that people are unable to publish failed replications, but that people don't even try to replicate because there is little prestige or funding for it. I think we need greater rewards for successful and unsuccessful replications, and in the latter case, greater negative consequences for the people who did the original work.
Having a journal for replications (why exclude successful replications?) might help, but in my opinion something more dramatic will be needed.
If you want food for thought, see Robin's paper
This just came up on HN: How To Publish a Scientific Comment in 123 Easy Steps (pdf)
Ideally, an author can be notified of their mistake and publish a retraction (it should be their responsbility), but it seems that some authors would rather defend work they know is flawed, or do nothing and hope their mistake goes unnoticed.
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.]