This is just what I needed. My replacement 920 came in today. This one doesn't bang around when you move it, but I found an extremely annoying problem with it when I plugged it in. The screen goes numb. Scrolling becomes very difficult, apps open without me touching them, and when it does scroll it's really laggy. I don't remember my old one doing this, did I get another lemon?
High sensitive touch on or off, it happens. I've done a soft reset, hard reset, etc. It does it no matter what.
I have this problem with my smart phones whenever the wrong type of charger is attached. For some reason all my windows phones (focus, 900, 920) have all acted funny whenever the wrong power adapter is attached (doing the same things you describe). If your using the adapter that came with your phone, then this doesn't apply. Best of luck though.
If you are having that issue using the included Nokia charger, I would say you have a problem with the phone or the charger. I had that kind of issue with my ZUNE HD if I used non Microsoft chargers. My touch on my first 920 was flaky when plugged it into the charger, but it turns out that device had a defective screen with a quarter inch across the middle where the touch did not work at all. My replacement phone touch works perfect when it is plugged into the charger or on top of the wireless charging pad.
This is a common issue especially with Windows Phones (the OS itself has nothing to do with it... maybe because of the similar components used). If you use a charger that doesn't have EXACTLY the same specs as the original one, screen will go nuts and sometimes the phone will get hotter than usual as well.
Solution? Use the supplied charger, or at least one with exactly the same specs.
Charging via the computer USB doesn't seem to cause troubles, no matter which cable you use.