this is a problem known around our stores as "Ghosting." essentially, it is thinking someone is pressing the screen when its not.
this is usually caused by one of three possible issues. in order of likelyhood, they are;
1) A short in the touch circuit. (most common, and replacing the digitizer/touch panel is the way to fix this)
2) A connector problem. Always try disconnecting and cleanning the connectors first, as it could be a dust/debris causing it. If cleaning does not work, try replacement connector.
3) Touch Control IC failure. Board level chipset issues. you will need to solder a new IC onto the board to fix this problem