Yes, it seems a major problem. My 2 month old Z3 Compact developed a hairline crack at the bottom of the screen rendering the whole phone useless. I'm furious & gutted as I really do love this phone. It's just fragile and needs real protection. Mine is under warranty and I'm hoping that it will be fixed free of charge as, despite what they say, IT IS a well known and common issue. There's even a Facebook page set up with 3,000 members already!! And other news stating:
"On smartphone forum XDA-Developers more than thousand Sony Xperia Z3 users report cracks in the front and back of their phone. It’s not the first time Sony has issues with the screen of Xperia phones, also the Xperia Z suffered from similar problem.
About 25% of the Xperia Z3 and Z3 Compact owners that filled in a survey started by an XDA user have issues with broken glass. Some suffer from just a single crack horizontally, vertically or diagonally but 12% of the complainers report to have multiple cracks and even ‘spiderweb’ resembling cracks.
A user has also started a Facebook page for users with cracked screens, a post asking for users to report cracks in the screen of their Z3 resulted in a long list of comments with pictures of damaged phones.
Also on the Sony Forums dozens of people complain about the glass cracking for no apparent reason. Unfortunately for many users it’s hard to proof the glass hasn’t cracked by falling. Continuing to use the phone is for most users not an option as the touch screen becomes unresponsive even with small cracks."
Such a shame as everything else in this compact little phone is awesome in my opinion. Quick, responsive, great screen resolution, awesome camera, waterproof (untested yet!) and guess what? Nice and compact. Just fragile glass screen issues.
I would advise a tough glass tempered screen protector and then a durable, hard, shock absorbing case that allows for magnetic docking charge and properly protects all of it's somewhat delicate framework. Still haven't found a 5 out of 5 one yet.....
If Sony don't treat me with a decent level of customer service I will be forced to make a complaint and let this well known issue even more 'well known' for users choosing whether a Xperia Z3 / Z5 / Compact is right for them.