I have recently sent my Z3 Compact in for the third time due to the screen popping issue and fourth overall as it had been sent in for GPS repairs. Originally the person on the live chat wasn't helpful at all and I had to push to get escalated after he originally said he couldn't escalate the case, he acted more like a roadblock to my solution than a help.
A few days later I got an email from the escalations stating that I could exchange my Z3 Compact for a new one or upgrade to a Z3+ so I choose the upgrade and ring up to inform them. I was then emailed to put in a repair request and everything would be sorted.
The next day the phone was picked up and I thought I'd have my new phone within days as all they would have to do was go "Yep that's broke, send the new one" (the screen was very obviously falling out). Now 13 days later I finally received the phone. What I also found peculiar is that the tracking they gave me on the outbound journey said the phone was signed for on 7/09/2016 whereas they didn't say they'd receive it until the 13th!?
They've now sent me a Z3 Compact instead of Z3+ as they offered and I'd asked for so I've rang up and they've said that the escalations will contact me within two days.
So it's now been 18 days since I contacted Sony about the issue and it still isn't resolved, hopefully it's going to be sorted quickly when escalations are on it again but my hopes aren't high.