Trying to troubleshoot, I was using https://meta.stackoverflow.com/network-login-help?.
With my regular profile and addons in Firefox (26 64bit Mozilla build for GNU/Linux), I get: scripting OK, cookies OK, messaging failed, storage failed, communication skipped
With a clean profile in safe mode, I get: scripting OK, cookies OK, messaging failed, storage OK, communication skipped
With a clean profile in safe mode, navigating from tex.stackexchange.com to the meta site via the top bar menu gets me a security warning that the certificate does not warrant the domain and the "get me out of here!" button.
With my regular profile, logging into the meta site immediately returns me to tex.stackexchange.com and even when I appear to be logged in on meta, I cannot comment/vote etc. because the site thinks I am not logged in.
With my regular profile, I cannot view images from http://i.stack.imgur.com in place but they work fine in a new tab.
I am especially curious about the problems I'm seeing in a clean profile with no addons.
Any suggestions for just pinning this down would be great. One problem is that everytime I think I've found a pattern, it shifts. I restart the browser and stuff changes. Or just stuff changes. Even with a clean profile. It is driving me nuts - it all worked beautifully until just a couple of days ago and now everything is crazy.
Further info/history at https://tex.stackexchange.com/questions/153107/problems-with-se-site.