Trust is the biggest issue, it is not privacy.
If trust is present, all other issues go away. See this article, LAPD wants to make drone program permanent and expand uses for the aerial devices.
I think that the Los Angeles Police Department is taking the right path. Start small. Involve the community. Report back on how and when the devices have been used. Ask for permission to do more.
While police have the toughest issue, this can apply to any public agency. Even when drones become more "socialized" with commercial applications, public agencies will have to jump through different and more stringent hoops.
More technology challenges are coming. Facial recognition is here today and the use of Artificial Intelligence will be another battle.