I don't have a good solution/answer, but think the following should be considered.
If you ask different publishers whether publishing blind reviews is appropriate you will likely get different answers.
The timing of publishing such reviews surely matters. If you publish reviews after final resolution of the paper's fate, compromising the blind nature is probably moot. Neither the author(s) nor the reviewer can influence the other improperly.
Longer term, if the blind review process is undermined by (too early) publishing of reviews, something will be lost and games will be played that undermine the whole process. There are valid reasons for blind reviewing. Among other things, saying something bad about a paper's methodology or results will often, I think, be misinterpreted as saying something bad about the author(s). This could have very bad long-term consequences when people start to argue in public about things that should have been settled.
My personal view is that a paper should stand on its own, without the commentary of others. If it doesn't, then it isn't a very good paper, and those issues should have been settled during review and rewrite phases.
I wouldn't publish any review, but that is just a personal choice that I'm not yet willing to recommend to others. But if it is done, I'd suggest that it be with the knowledge and permission of all parties: reviewer, author(s), publisher.
On the other hand, I don't think there is any issue about someone who previously reviewed a paper commenting in public on the final version of the paper. You would certainly be permitted to do that had you not been a reviewer.
For what it is worth, there is an alternate process for improving papers that is used in the patterns community to improve patterns papers. It is called the Shepherding Process (warning: PDF). The paper at the link explains the process, expressed as a pattern language. The key element is that it is not blind reviewing, but a cooperative, iterative, process to improve the paper.