I myself have tried to update to 8.0.1 and have experienced “you are no longer connected to the internet “error. My friends over at iDownloadblog got it the worst, their cellular and Touch ID stopped working. I would recommend holding off on it until the issue is corrected. It was supposed the correct the HealthKit app and more which are listed below.
If you were already affected here are the steps to downgrade back to 8.0.
Step 1: Download the iOS 8.0 firmware for your device via our download page.
Step 2: Turn off Find My iPhone on your device if you have it enabled. Go to Settings →iCloud, and disable the Find My iPhone switch.
Step 3: Connect your device to a Mac with iTunes installed.
Step 4: Open the device page on iTunes, and hold the Option key (Shift for Windows users) while clicking the Check For Update button. Find the IPSW firmware file that you downloaded in Step 1, select it, and click Open.
Step 5: A pop-up box will tell you that iTunes will update your iPhone to iOS 8.0 and will verify the update with Apple, click the Update button. Wait until your device updates, and enjoy your iOS 8.0 installation, with working Touch ID and cellular data!