I can't say that I've experienced anything like this myself.
After the factory reset, did your phone do the same thing before you reinstalled all your apps? If not, it might be a rogue app. If it still did the same, it sounds more like a hardware problem - maybe the touch sensor has some breaks or dodgy connection that's registering false touches.
Other than swapping the touch interface/screen yourself, you might have to send it off to get it checked/repaired.
Rhyan