An article in Slate, The Killer Robot War is Coming, describes a few areas of law that eventually will need to be addressed.
What are the limits on local governments using drones for occasional or even continuous surveillance of individuals? Your city police could never afford to put 24/7 surveillance on more than a few people and then only for a few days. With drones, it will be easy to monitor someone constantly for an extended time.
What limits do we wish to place on the president for using drones for deadly attacks in new situations? Might a U.S. president start a conflict on his own more readily if it can be fought with drones instead of putting pilots or soldiers in danger?
How will we control international usage of lethal drone attacks?
Check out the full article for an extended discussion of the issues.