The greatness of Broken Windows policing (for NYC) was the realization that the minority population was composed of a modest number of criminals, and a very large number of non-criminals, that the distinction between "big criminals" and "petty criminals" was to some degree arbitrary, and that if you started sweeping up, interrogating, searching, and warrant checking all the squeegee men, dope smokers, three-card monte artists, and taggers that you would find a lot of people who you could send to Attica for 20+, making everybody a lot safer.
Wilson and Giuliani did not understand the familial and tribal relationships among the criminal and non-criminal people, and I don't know that Rudy ever "got" why blacks hated him for making their persons and property so much safer, but it is what it is.
Cleaning up the city was actually a secondary consideration for “Broken Windows” policing. The primary purpose of that policing model was to arrest as many petty criminals as possible for the sole purpose of getting their records (especially their fingerprints) on file. This served two purposes: (1) to cross-check these records against unsolved crimes; and (2) to have additional evidence if/when the petty criminals committed serious crimes down the road.