iPad Touchscreen freaks out & screens self-registering

I exactly encountered an issue with my iPad. When its screen got excessively dirty with my fingerprints, the touchscreen would register touches without actually touching the screen. iPad will open or close keyboard quickly, zoom in/out Safari rapidly. Then I cleaned the screen and rebooted the iPad, this can stop this behavior until the screen gets dirty again.

I think that it may be caused by my hard presses of the glass. This will leave a distinct finger print wherever I pressed on the screen.

Now I don't even apply any pressure to the glass. Just make as little contact as possible. The screen is fine. If this method still can't fix it, you'd better do a replacement.