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I have sent it to the service repair center and they send it back to me saying that the problem was solved, but it wasn't true I am still experiencing it. I am suspecting that there is an issue with the apps I am downloading because I made a call before downloading apps,to see if the phone was working, and it was working ok but after that I downloaded the apps tried to make a call after that and the screen turned black againg and I couldn't end the call...
I am definetly thinking about scrapping my phone 
This problem IS NOT SOLVED!
I bought my Z2 (D6503) in 03/2015, updated it to Lollipop 5.0.2 immediately at the very first start up. I have the exactly same problem as jomanaes: when pressing call button the screen goes black immediately, before even raising the phone to ear, therefore making the call management / call ending difficult. Requires TWO pressings of power button to wake the screen...slow and difficult. Also, the auto answer when raising the phone to ear does not work (is selected from settings), which speaks of error in the proximity switch.
I have run all possible tests and suggested solutions: *#*#SERVICE#*#* proximity switch test shows "on" within a second of starting the test and the switch stays on, like jomanaes says, is stuck. The diagnostics in "about phone" - "troubleshooting" - "tests" - "ear proximity" gives similar results: indicative vibration starts immediately when starting the test and remains on until finishing the test.
I have already reinstalled the software via PCC (selected the blue highlighted option of faulty software). I also tried the boot in safe mode: the problem remains and all the diagnostics and tests give the same results.
It's a pity to have this type of bug in an otherwise perfect phone. Any new ideas or suggestions???
I have shipped it (for the second time) to the Sony Repair Centre in the UK.
I picked it up today, seems to work for now but I haven't installed any apps yet (I am affraid to install them) I hope it doesn't crash again when I decide to install whatsapp.
Last time, after I installed whatsapp the problem started to occur.