Screen lock up and unresponsive and all you can do is lock or restart. I've had this issue on my 6+ since the first iOS 9 release. After a few updates thought it was hardware, went to the apple store and they replaced my screen. Same issue still occurred, they replaced the screen again. Still have this issue to date, now I'm out of warranty.
It seems to be getting worse lately as well. Frankly it's EXTREMELY annoying and makes me want to sell the phone (waiting on the iPhone 7 but will I last 4-5 more months... stay tuned...)
I've owned every single iPhone from the very first (always skipping the S models) This 6+ is the only one that's ever given me so many issues.