I've had this issue with my 1520 bought in around Feb 2014. The phantom touches began about three months into my purchase and have been bothering me ever since. The first time it happened, I figured it was a software bug. I let it go. It began recurring every week or so seemingly like clockwork, and as much as I was sure I was wrong, I found myself leaning toward it being cause by a virus of some sort. I did a hard reset just to be sure. It seemed to solve the issue for a while and I quickly forgot about it. a week later, the problem was back and it was worse! I began checking the internet for answers. Nothing I tried ever really worked.
I noticed a few things:
Firstly: The screen ALWAYS registers phantom touches toward the lower edge of the screen. Generally around the "Back", "Windows" and "Search" buttons. If playing a game for instance, the game would scroll in the direction of the touch (if the touch was on the edge of the play area).
Secondly: The Phantom touches would ALMOST ALWAYS occur when the phone was fresh off the charger (I use wireless charging most of the time)
Thirdly: The Phantom touches usually occur when the phone is hot.
Fourthly: If I tilted the phone ever so slightly so the lower right corner was pointed downward, the phantom touch would go critically insane! (I know this sounds like voodoo).
Lastly: Locking and unlocking sometimes (but not always) corrected the problem.
It's odd, but nothing seems to make any sense. I am not sure how the device is built, but considering the top half of the phone heats up, the phantom touches occuring at the bottom edge of the capacitive screen,the odd madness during tilt.... it seems crazy.
Anyway, I read somewhere about the screen-slap technique. You hold your phone face up and give a firm slap to the screen and it somehow resets the phantom touches. I tried it often. You can feel the tactile vibration when you slap it. it works half the time, but does not always work.
I found that just holding the phone face up and placing your palm gently over the top half the of screen causes a couple of tactile vibrations after which the phantom touches stop. The suggestions earlier about it being related to electrostatic grounding makes sense and is probably a secondary cause, I however believe that it's due to expansion of contact surfaces due to heat. I've never had phantom touches on a cold phone thus far. It only occurs when my phone is fairly warm.
Just to note, My phone shipped Black, It's been through all the updates and is now sitting on Denim. None of the updates did anything to solve or even reduce the phantom input problem. It reeks of hardware.