So the occasional "collateral damage" is OK with you as long as there aren't too many and as long as the main objective is met?
Collateral damage is not the issue. Cops make mistakes. They are humans put in difficult life-threatening situations. You can't take the mayor to task for the mistakes of a police officer.
Take a look at DeKalb County in Georgia. Same problems with the police there.
Unless he pulled the trigger himself I doubt it will hurt him. New York without Giuliani was more oppressive than with him.