This weekend I will not have the time to add another long post, partly because I will be traveling to Rio to present in SoCG 2013 a result about point-circle incidences in (see here).
I did add this new webpage to the blog, where I will place relevant pdf files. For now it contains my survey of open variants of the distinct distances problem, and the best known bounds for them. This document contains the problems discussed here and here, and I plan to extend it soon.
Finally, a paper quite useful to us all can be found here.