I've often thought that on a touch screen device the OS should ignore touches on buttons/popups that have been on screen for less time than a human could reasonably have observed it and chosen to interact with it. If I touch the screen 0.05 seconds after a button appears, I was probably _not_ aiming for that button.
In fact, now I think about it, this has happened many times over the years with traditional mouse drive interfaces too.
I'm sure some power users would like to shorten the 'reaction time delay' or even remove it entirely so I guess that should be an option as well.