Could be a digitizer issue, sometimes if you have a residue or water on your screen it will register it as touches. Make sure your screen is completely clean. In the settings of the phone, go to developer options then scroll down and turn on show touches and/or pointer location. Those will show you the problem areas that keep registering touches. If it isn't caused by a dirty screen, it could be a hardware issue. Try an FDR (factory data reset), of that still doesn't fix it, you will probably have to go to your phone retailer and get it replaced. (Hardware defects should be covered under warranty as long as there is no water damage found)
I've had the same issue, mostly due to grease from working in restaurants. I'd have to clean it off real well, and restart the phone if I didn't have the patience to just wait for it to sort itself out.
Excellent posts by both preceding members. I've found as well that dirt and oils tapped along the glass digitizer's edge can cause false reads or "ghost typing". A thin piece of rigid plastic like that used in packaging, cut to a triangle point, can be slid down between the glass and Bezel (metal surrounding sides), and if gently slid along the edges it can bring up the offending matter. This was especially true of the earlier generations of digitizers, such add those on the OG D Droid, but seen to be less prominent with the newer ones.