OK I think I found it, after spending another 5 hours setting up/configuring my phone. I did the factory reset via Clockworkmod, phone reboots and works perfectly (drag to unlock, dismissing calls). So I start reinstalling apps, configuring accounts. Everything is great, I get everything installed, organized into folders (I have a lot of apps I use). All the while as I'm installing apps I'm checking the unlock and its sitll working. I think it's a fluke, then I start Light Flow, recover my saved settings and let it use root via SuperSU. Now the lock screen is broken. So it's either Light Flow or its SuperSu. Sigh. I'm going to reset again, switch to Super User and see if that makes a difference.
Leebo, Are you using either SuperSU or Light Flow?
Edit: OK so I missed your earlier posts (forgot to refresh my browser and go to page two!). I can confirm it is simply turning on Accessibility for an app (my culprit was Light Flow - I didn't even have to setup the app, just turning on accessibility broke the lock screen). Turning Accessibility back off fixes the problem, which is good, since I did a back up before resetting my phone.
This is a pretty big problem - I can't use my Pebble watch or Tasker or a number of other things. Does this happen on any version of the One? Mine's the Developer Edition. Is it only happening on phones with unlocked bootloaders or rooted?