What happens when your screen orientation becomes stuck? Are you still able to move around the phone (go from app to app, use apps, et cetera), but just in a fixed orientation? I've run into a few problems where the orientation gets stuck, but only within apps; and then I just exit the app.
Also a strange thing happened in the YouTube app yesterday where I brought up the keyboard, and it was in landscape (and not the new 6 Plus landscape keyboard either, but an old school iPhone keyboard but stretched across the width of the screen), even though the rest of the app was in portrait mode.