I've been having the crazy phantom touchscreen freakout screen issue for 2 days now, off and on. I read what Steve H mentioned about the protective plastic coating behind the screen causing the issue, however in my case, that plastic coating has been removed for months.
Additionally, my phone first started exhibiting this issue when sitting in a cool, dry environment, and humidity/temperature do not seem to impact the frequency of the problem, therefore I do not believe these to be the root cause.
I do, however occasionally use aftermarket chargers, and one of my original chargers has a wiring issue where it will sometimes carry a very poor connection through to the phone, causing moments of extremely rapid connect/disconnects.
In my opinion, problems with inconsistent charging and/or voltage seem to be the most likely culprit in catalyzing this behavior, however, based on the frequency and volume of users having this problem, I do believe there to be an inherent flaw in the D1's design.