I did just start looking for the solution when Rusty replied and found the problem before Inspector's reply.
I'm sure it was part of a dev experiment or a test and the changes were never rolled back.
A check for user uri page's session data was disabled.
As a result all logged-out visitors were unable to post any data back.
Registration, posts, contact form and logins (i've been always able to login but) were affected by the error.
.:: I met php the 03 December 2003 :: Unforgettable day! ::.
Server specs (Server OS / Apache / MySQL / PHP / DragonflyCMS):
CloudLinux / Apache 2.4 LSAPI / MySQLi 5.6 / PHP 5.6 / DCVS