My iPad2 (over a year old now) has started acting up. It types by itself or sometimes opens websites randomly when I am in Safari.
I backed it up on iTunes and reset the iPad2. That did not help.
I then upgraded to iOS6 and that didnt help either.
Have you cleaned your screen? A dirty screen can cause this issue. If your screen is clean then do a soft reset. Hold the Power and Home Button down untill you see the Apple Logo, let go. Let me know if that worked.