My iPhone is running 8.3 and it's having the same problem, which as others reported started when I installed iOS 8 months ago. I don't use FaceTime, so that's not the problem.
If I turn the phone, nothing happens. I have to wait while it tries to figure things out and then finally switches to landscape. By then I've usually given up and switched back to upright, which means that just when the screen finally shows up at landscape, it realizes it's got to go back. This process takes minutes, not seconds, and it's extremely annoying.
Like others, I've powered off then on; done a hard reset; restored from backup. Nothing helps. It really has reached the point where I'm ready to throw the phone against the wall.