An issue on which many are confused, and few productively cut through the noise. If you are nervous to explore the issue (or any other), I am on your team. Our mutual goal is to discover the ground truth.
Bad behavior / minor criminality is tolerated in NYC to a level that exceeds other places I've lived. Jumping subway turnstiles, graffiti, littering (especially cigarette butts), extremely loud music in public spaces, extremely loud car engines, blocking the box etc.
While actual crime is quite low, the *feeling* that crime might happen is always high, which is probably why people are constantly on guard. And with a culture of "mind yo bizniz," a lot of crime that does happen goes unreported here.