Contact reviewers/authors after the end of the review cycle for follow up
As has been stated in the comments to your question, contact between author and reviewer once the review process is complete is no issue. In a double-blind system this hinges on establishing the contact and in that case, as stated by Nate Eldridge, it will have to be a contact from the reviewer. In other cases where authors are known to the reviewers it depends on the willingness of reviewers to reveal their name.

The editors obviously sits on the information that could connect the two under any circumstance and you can of course always ask an editor to forward a request to an anonymous reviewer. As an editor myself, I am not sure I would be altogether happy with such a development since it would mean a lot of communication back and forth concerning matters with which I have nothing to do. I will add that many if not most editors do this on their spare time or time they take from their own research and are not salaried to do the work. This is why I would think twice about making the request and make sure the reason is very good and of such interest that an editor will see benefits to science to make the effort. As you probably realize, doing this once is no big deal but if it becomes routine it will occupy much time for an editor. I would then clearly opt for changing the review system to not be anonymous and try to convince the community that such changes has benefits worth considering. Another option is to keep the review process double blind but then provide all information to both parties once a decision (accept or reject) has been reached.