Something seems to be very wrong with local search, at least in my country. It is showing results that are totally unrelated to the searches. And I'm not talking about a few sites that managed to show there, I'm talking about a total mess.
For example searches for hospital+city is showing restaurants, coffees, libraries, etc Searching for police+city shows pharmacies and hotels while searching for electrician+city I see a church, a library and a university.
It's never been 100% precise but it looks like its 100% broken now.
For the Onebox to be accurate, I think you need to search for something of which there would be at around 7 results (or at least more than one).
For organic results (We have only one hospital to my knowledge in my suburb), I get a map result and a few results directly tied to the hospital but then lots of directories about hospitals (including ours).
Ditto for Police+suburb.
I see that for large city centres there is a onebox but lower in the page. I am not seeing the issues you are seeing. I guess you should use the "Dissatisfied? Help us improve" link.