Android phone taps touchscreen on its own
Yes. Seems there is a problem. The touchscreen takes inputs that was never made. Have a look at this http://www.thinkdigit.com/forum/mobiles-tablets/122921-official-android-discussion-thread-73.html#post1836923

There are various problems of Android that LG ships on the P690. I'd suggest installing a good custom ROM, which should fix the problem if it is not a hardware issue.