I guess we cover both of these problems at once. We always have a couple of bags tied onto each leash.
I will say, though, that if they fill a bag when we are starting on a beach hike, we mark the spot with a tall piece of driftwood and come back later for it. Putting that marker out let's others know that we do intend to take our "presents" back with us when we return.
As far as kids crossing camps of others goes, if nobody tells them that they shouldn't, how are they going to learn? Their parents obviously don't tell them.