I'm all for natural solutions to problems. Having goats eat weeds is how people years ago "mowed" the grass before the lawnmower was invented. The droppings ought to re-fertilize the ground. THis is a much better soution than spraying herbicide that not only affects the unwanted plants, but the wanted, and beneficial ones as well. It also frequently ends up washing off into rivers and streams, and affects areas several miles from it's intended location, not to mention drinking water. Not to mention goats are rather friendly, fun creatures. My cousin has some on her farm, and they are great!
My only worry is if the goats are used to keep the weeds down along highways and roads that they may wander out into the path of traffic and get injured, or cause someone to swerve and loose control of their vehicle and injure themselves.