1) Unlock process: When the fingerprint reader fails it now takes several presses on the home key to get a keypad to pop up so I can input my code. With previous versions I could just swipe when I knew the fingerprint reader would fail (e.g. wet hands).
2) App updates: When apps are updating on my phone it decides it really wants to stay on the home screen. I can swipe to get to the other screens, but it goes back before I can tap any apps. Also, when I can get into an app they tend to lag and crash more when updates are happening in the background.
3) Control Center (bottom menu): Trying to slide the brightness or volume controls on the control center menus usually gets interpreted as a swipe to the next control menu. I have to be very precise when touching them for the sliders to actually work.
4) Safari: Auto-hide of the control buttons does help page visibility, but showing them seems to be glitchy as hell. They appear and then disappear before I can move my finger to tap them.
5) Crashes: At least daily now the whole phone crashes to a black screen and then comes back to the lock screen a few seconds later. Seems to involve location services.
Also, not exactly iOS 10, but the new Watch OS completely broke the usability of the Weather app for me. Something that was fairly intuitive and useful is now cumbersome and basically useless to me.