It all started on Cm 12 after clock wouldn't stop stopping. I had some wicked ghost touch issues and then I discovered that I had dead spots on my screen. Any fixes other than replacing the screen?
Try reflashing a stock ROM and see if they're still there. If not, there's a bug in CM12 for your phone. If they are, it's time for a new digitizer. (You don't have to replace the whole screen - but please have t done by a professional, it's easy for an inexperienced person to destroy the screen when replacing the digitizer.)