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Home doesn't turn to landscape mode when the phone is turned.
Only when connected to the dock.
What's up with that? Will it be fixed?
It's not that its broken, but that's the way the Home launcher was designed, to only go on landscape when connected to the Dock, it has been requested before to made this available even when its not charging at all, but it doesn't seem that it will happen, there are alternatives
1. use a different home launcher
2. use an app that will force the home launcher to rotate
3. mod the home launcher so it will rotate (check the XDA forum)
It has always been like this for Xperia phones. I think they come to a conclusion that horizontal mode homescreen does not provide a good enough experience since it's too small. Although the auto-rotate is not enabled on Xperia phones, it's enabled on Xperia tablets.
The alternatives are as mentioned above. 
Edit: And I forgot to mention that landscape mode is also enabled when phone is docked.
And yet, the pictures of the SCR10 case for Z2 show a landscape home screen 
Totally agreee.
Considering the polish and care taken in the build quality, elsewhere in the Xperia Z2, not to mention the marketing of the device.
Its hard to believe that Sony Mobile chose to selectively support Auto-rotate screen.
Which asks the question, why give us the option to select Auto-rotate screen, when the phone does not completely support it?
It makes an otherwise polished and restrained experience, crude, and clumsy at best.
Which is completely at odds of what is arguably the mosty stylish smartphone on the market today.
Even more so, that its also found in the previous ZL,. Z, and SP.
Sony Mobile need to be more consistent with their implementations, if they want to win over, and retain new owners from Apple and Samsung.
Rather than just the Sony faithful.
I bought one of these covers and then was disappointed that the phone doesnt actually support the rotatation of the home screen which that picture shows 
I have been using this app and it works a treat:
https://play.google.com/store/apps/details?id=com.spydiko.rotationmanager
Set it to force-auto. Done.
I also have problems with the screen rotation. In home-mode it will not rotate to landscape. Only when I use the mhl-cable for connection to my TV.
ajpiels