There might also be a war on licensed onces as well. UAVs currently are used mostly in combat zones, but I think it won't be long before they are zooming above restricted govt. areas, large cities, are used to track and chase fugitives, and even by small town cops to patrol and issue traffic tickets remotely.

As this happens there will be some who will take it as a challenge to destroy, capture, and most of all, to take over these drone. That does not entail injuring or harming an officer or a human so those who would never try to mess with a real helicopter or police cruiser might not have a problem messing with flying remote robots.

There could be a cat/mouse game going on between law enforcement and criminals running UAVs (eg. to run drugs). Miniature dogfights?

yes and that will be the Last War. the one that Skynet wins. :)