I have this same problem. As someone stated previously, I think this is related to having too much index finger skin touching the screen. For some reason the screen registers all of that finger skin as multiple points touching the screen and bounces between the two points.
I also have this issue on my Lumia when it's plugged into a charger.
My old LG did the same with certain chargers, it looks like the Capacitive screen is picking up interference/feedback from the charger itself
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Last Nokia: Nokia Lumia 800
Current Phone: A Non Nokia Device
Previous Phones:Don't Ask ;-)
I have the same issue. I made another youtube to show other people what I meant.
I was planning on going back to the phone shop tomorrow to get an exchange but I won't bother if all the phones seem to have the same issue.