Then, after an unlucky drop, my screen was broken, so I got the screen repaired. After approx. a week my screen got more and more its own life. At the end the phone was totally unuseable. The repair shop replaced the screen again, since then it just apperars from time to time like before.
I think Sony has some issues with these screens. My S2 which I had before the Sony had never such issues, even if the screen was quite dirty. Maybe thats why they introduced the Z3 so fast?
Here you can see the "amok screen". I enabled "Show touch" in the developer options.