Permanent login via 'Remember me' functionality is broken in Joomla if 'System - Cache' ('System - Page Cache' since 3.4) plugin is ordered before 'System - Remember Me' plugin.
Sometimes after update to Joomla 3.4 your sites can stop working if you are using native Joomla multilingual functionality.
How much time did you spend adding correct ALT and TITLE tags for images of your Joomla website? If more than 5 seconds - next info can be interesting for you.
Probably you faced a problem when using Joomla SEF URLs and once menu items aliases are changed or a site is moved to new domain or subfolder - all links to menu items are broken in your articles.
Joomla 3.2.0 is a result of terrible coding and total irresponsibility: users registration and password reset are broken and passwords are not recognized. Please note that Joomla 3.2.1+ doesn't have these issues.
We suffered from this a couple of days and finally propose a solution, though you can just install Joomla_3.1.6-Stable-Update_Package.zip and downgrade.