After Rooting my phone, I get a black screen, followed by "[app] has stopped working" for every application, any idea what could be going on?
I had the same problem when I flashed cmw12.1. 
I backed up that Rom and when I rebooted I got same message as you.. Everything saying "stopped working!". 
Later I noticed that my nadroid backup was on internal storage and I was running out of space. 
I deleted that backup and everything went fine. 
Move that backup file to external sd card and try rebooting again.. 
Hope that would fix it :)