Read through this entire thread after much frustration... I tried ALL advice to correct this...
iPhone 6 (64gb) iOS 8.1.2 Brand new! Bought this phone today (12/9) worked fine on my iPhone 5 with iOS 8.1.2
I did NOT do a restore to transfer data, I treated this like a brandy new install.
I can swipe down in the Notification Center, however I cannot swipe up at all...
Camera swipe from lock screen seems to be fine, no issues.
Swiping up to get to the notification center seems to be the only issue so far.
I also just noticed that if I turn the phone to landscape view, in app, then swiping up to access the control center works just fine. No luck in portrait view.