The same exact thing happened to me with my launch-day Surface RT. At first, the 'touch cascade' (as I was calling it) would happen every couple days or so. Suspending the device and resuming would clear it. Then, it started happening every day, and then multiple times a day... eventually every other swipe from the right side would result in a cascade.
Towards the 'end', I also noticed that touch precision on the right side of the tablet was diminishing, and I had trouble activating buttons on the right (i.e. the delete button in the mail program).
Thinking that the something in the firmware got hosed, I did a reset on the tablet. When it came back, it seemed to be fixed. "Great" I thought... until I started reconfiguring the tablet back to how I had things set before the wipe. Now, when using the split keyboard, it was impossible to get the 'p' to register. Each press directly over the 'p' would register either to the right or left, never triggering 'p'.
This was really started to smell like a hardware problem...
Before I gave up though, I figured I would try to calibrate the touch screen (get to it via the control panel). I had limited success with this, after calibrating a good dozen times or so. I could never get it to work perfectly. I could get the 'p' to be recognized, but then wouldn't pick up certain swipes, etc. In the end, I wound up sending it back to Microsoft for a replacement.