This is pretty incredible! No more need to buy gyro-stabilizers for these cameras (if you are posting to Facebook). I've found the Facebook 360 viewer is more intuitive than other viewers out there.
As I'm reading this announcement they have a nice solution for problem A - moving camera. Problem B and C results in jello-effects (assuming rolling shutter) and blurriness, respectively. There are research solutions for all of them (see e.g. "Dolly-cam" from Per-Erik Forssén et al at Linköping University). But for practical purposes you are still much better off if your camera is not shaking all over :)
Look at drones and compact cameras for examples: gimbals and optical IS beats digital stabilization every time.