Yes I started to have this issue when I updated my iOS to 10. It was happening more than frequently, especially when I needed to make important phone calls, looking at my recent calls, etc. The app would just freeze not allowing me to toggle within the different screens example (recent, calls, favorites, call/dial, voicemail) the screen was basically frozen, I would jump out by pressing the home button then back to the phone app, and again nothing would work, in some instances the app would just crash and then work. Another thing I may add on this is my emails will respond very slow when toggling quickly to have the mail go from unread to read, you literally have to wait until the complete mail loads and wait for the blue notification to disappear until selecting the next mail in order for it to register as "read". Not to mention the removal of slide to unlock, with those 2 issues occurring on my phone and with the removal and not leaving the option to add slide to unlock I found the best solution. I was able to downgrade back to 9.3.5 which it is still available if you want to fix these issues I suggest you downgrade to a much stable UI, until Apple releases a much stable version. Personally 9.3.5 works well so I wont be doing an update anytime soon.
Phone: iPhone SE
Version: Rolled back to iOS 9.3.5
Bugs UI Version: iOS 10.0.1/10.0.2