There have been some other users that have reported this weird behavior over the past year. You could try restoring to factory settings but - I agree with Marian. I believe that your best bet would be to make an appointment at an Apple Genius bar and let them see this strange behavior. From what I can remember - it turned out that there was no fix for this "phantom touching" and the iPads had to be replaced.
Someone else may come along with another idea - and for your sake I hope you find a fix here, but I wouldn't put too much time and effort trying to find a solution on the internet before I would head down to the Apple Store. - just my opinion ...