We have the same problems everywhere in NYC. We have an unbelievable number of police on the force (corresponding to much higher crime levels of the past), yet there's very little traffic enforcement. People routinely drive recklessly, enter areas they're not supposed to, park illegally in travel lanes, bike lanes, or sidewalks, etc., and there's little risk of anything happening. Even worse, we have a huge placard abuse crisis where many tens of thousand of different government employees (cops, firefighters, teachers, city workers, etc.) get these ridiculous placards that essentially make them immune to parking enforcement, even when driving their personal vehicles in non-emergencies. The police (who largely live outside the city and drive to work) thus see this as one of their perks and they are loath to do anything to fix it.
So the only solutions that will work are those that don't require the police to do their job. We need red light cameras at every intersection and speed cameras on every road (they'd very quickly pay for themselves), and we need physical protection installed everywhere so that cars cannot even enter bike lanes or drive up onto sidewalks. It's sad that this is what it's come to, but absent getting a non-car-based police force who live in the city who are actually interested in protecting us against drivers, I don't see it changing.