For all those folks that have problems with the random or crazy touch in their xperia z1, this little apk
dl-1.va.us.xda-developers.com/9/2/0/2/6/4/TouchRecalibrate.apk?key=zqEfpblUz0YKGPUqTvRAiQ&ts=1398353...
fixed to me! No root needed. Just be care to not touch the screen at the moment of the calibration. I found this solution in the xdadevelopers forum.
you can verify the permissions for this apk, is clean and secure. I did this on the android 4.3 but i know that it works on 4.4 too.
That's all. Be happy 
Bro seems like the link is not working 
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