Police or other government agents are already required to get a warrant before collecting information. It doesn't matter if it's a phone tap, an unmanned aircraft, or a GoPro on a stick! Is it necessary to re-iterate existing laws for every new technology that pops up?
The police are already prevented from using helicopters to collect visual information from places that would not ordinarily be visible. I can't see why drones would be any different.
I really think people are responding to the somewhat disconcerting idea of drones watching you from the air while you're out in public. Essentially, people are worried about cops having a more efficient way to do something they could legally already do: observe you while you are in public.
By what logic do you think the police are prevented from using helicopters to collect ordinarily unobservable areas? The main relevant Supreme Court case I could remember was Kyllo v. US [0], but in refreshing my memory, it seems that that case only applies to intruding the privacy of the home, especially with technology that is not widely available. In fact, two cases linked from that article [1][2] directly support the ability of police to perform aerial surveillance, but only for things officers can see with the naked eye.
As Stalin once said "quantity has a quality all its own", oddly apt for this situation.
It's one thing when public observation by the authorities is sporadic and rare, it's another thing entirely when technology makes it possible to track, record, and collate every single second of your life spent outside private property.
Imagine for a second what this might look like. If every time you were "in public" there was a video record, an audio recording, and a voice transcript (carefully filtered so that it was only of conversations that could be overheard, for example). We expect that when we are in public there is some loss of privacy, but not to that degree, not utterly. Such complete surveillance could track people's movements and relationships which would make many details of otherwise private information a lot easier to determine.
This is not only disturbing, it's a massive explosion in police power. Imagine how difficult it would be to avoid police monitoring if every doorway in all of the major metro areas and major highways are tracked by drones. Even if you were able to be in disguise a combination of kinesthetic analysis of your walking gait and physical characteristics and sheer process of elimination would put you back in the spotlight quickly.
Now, this sort of scenario isn't overly likely in the US, yet, but we should be sensitive of the fact that there are phase changes and qualitative differences that accrue due to mere quantitative changes in capabilities.
Drones are a relatively new technology. I'm sure some agencies are presently interpreting old laws very loosely. It's certainly worthwhile to spell out exactly what can and can't be done.