A few issues/problems
I just bought my Z today and am having a few issues with it. First, the automatic brightness doesn't work. That is if it is turned on/off from the menu bar it does not work at all. If it is changed within settings the brightness does change to a certain level and that's all it does. Second, the tablet is extremely slow installing some applications. I have owned many different android devices and never experienced the absolute slowness this tablet has when installing some apps. Not all apps install slow, but I had one take over a minute when it should have taken about 5 seconds. And finally when using the browser, the touchscreen becomes very unresponsive when downloading and installing applications. I try to scroll by swiping the screen and sometimes the tablet just completely misses seeing that input.
Edit - I tested the auto brightness some more and it does work, it's just not as sensitive as some other devices I am used to.
Edit2 - I think the slow install could be a bug with the custom skin Sony uses on top of the o/s. It's sometimes getting 'stuck' displaying the install message.