Share your experience!
Try to boot the phone in safe mode,see if the same occurs:
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
About the white circles,did you change anything in developer options?
First,I suggest you try a software repair with sony update service:
http://www.sonymobile.com/gb/tools/update-service/
If not helping,you should visit a sony service:
http://www.sonymobile.com/global-en/support/contact-us/
You could try to update,see if that helps at all.
the problem with the touchscreen have been very irritating in the past firmware, n also in the latest 4.4.
look at this thread, http://talk.sonymobile.com/t5/Xperia-Z1-Z1s/xperia-z1-touchscreen-problems/td-p/410611/jump-to/first...
even repair through PC companion or SEUS a thousand times, it doesnt help.