Had the exact same issue as Tim with the top left home button, and after playing a bit with firware up/downgrades (actually I was barely able to access the home button on the early firmware by tapping ~10mm to the right of it, but this was not possible with the new interface), I also got a replacement unit that is working fine.
Thanks for this post, I didn't find much info on this issue when googling, I thought I was very unlucky ^^
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