Apple Statement on iOS 8.0.1: We are “Actively Investigating” Bug Reports
We have received reports of an issue with the iOS 8.0.1 update. We are actively investigating these reports and will provide information as quickly as we can. In the meantime we have pulled back the iOS 8.0.1 update.”
We had to restore our iPhone 6 Plus to a fresh copy of iOS 8, which fixes the problem—follow our tutorial here.