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That sounds strange. Do you experience the same behaviour in safe mode?
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008
Or do you use any case/cover? If yes, I would suggest that you try to use the phone without it for a while to see if same thing occur.
i'm having the same problem too ,
touchscreen goes like crazy like you have the display really dirt with a lot of false inputs
and you can avoid it only by pressing the lockscreen button and unlock the phone again
veeeery frustrating
you can't play a game
you can't take pictures
unless you lock and unlock again the phone