My last update (I think). After doing the DFU restore to basically reinstall the operating sytem my iPhone 6 stopped misbehaving. It was doing wierd things with the touchscreen -- jumping around even when I wasn't touching it and occasionally locking up the screen. I turned all the analytics off after a couple days after the DFU restore and it has been almost a week -- still no problems.
To those that think Apple has some conspiracy going on, I'm sure I can't dissuade you. But having worked for a manufacturer for many years I've learned that it takes a lot more than you think to get a product right. And we can't just fix a problem overnight (ususually). And we usually have many other things to do at the same time. And our employees have lives too. That's the hardware which I think is most likely not behind these problems for most of us. When it comes to software, bugs are fun. "No software program is fully debugged. Attempts to debug software inevitably introduces new bugs that are even harder to find."
Apple, I've noticed, does not pre-announce fixes. Why would they? It's like your doctor saying, "hey, we got this cure for cancer that will be ready in 9 days -- just wait until then." And when 9 days go by and you hear nothing, you might ask. Then you get, "well, we ran into a problem ..." And so it goes. How long does it take to cure cancer? Come on! Tell me everyone! Apple does not know how long it will take to fix it. Or even how. Not until they are done. Which is on the last day.
The DFU restore fix -- if you haven't tried it -- makes the most sense to me. OS 10.3.1 doesn't screw up everyones iPhone 6. Why? I'm guessing the update process doesn't work so well for some of us -- maybe those with a 32 bit app still. Or a set of option combinations on and off. And so on. But reinstalling the operating system from the ground up works in fixing many computers that were working but stopped working well after an operating system upgrade or patch.
So try the DFU restore. See an earlier post for instructions or do a web search.
Good luck all!