Ballpark is around two seconds from making a control input (such as "begin orbiting around this point") and getting the feedback (like seeing the plane turning on your screen). You have to simultaneously stream full motion video from every drone flying over Afghanistan halfway across the planet via satellite-- not really an easy task. The latency sensitive parts such as taking off and landing are obviously done from nearby the physical location
If he target is moving at a constant trajectory it's probably fairly easy to compensate for a couple of seconds lag, computer could probably do this without much issue.
Then that would be "collateral damage" which is such a lovely euphemism for "we blew a bunch of innocent civilians to chowder but hey we are the good guys".
It's not so much a latency issue but a field of view issue. Cars don't really go that fast and you'll see them coming way ahead of time as long as your camera is zoomed out far enough. There are procedures in place to reduce the amount of stuff like this happening, but they haven't always been in place and they don't work 100%. But it's not like it's an issue that nobody has ever thought of, it was happening even before the rise of the drones: http://en.wikipedia.org/wiki/Grdelica_train_bombing
Those missiles are laser-guided, and the Drone flies following way-points. The only time were the latency actually comes into effect is between the firing order and the actual launch - Hellfires are F&F.