The NYC DOT is aware of NYC’s bridges and their repair/maintenance requirements. There is no danger of collapse.
In every case of catastrophic structural failure in the U.S. (at least for the last several years) the cause has been poor engineering (the Minneapolis bridge, the Kansas City skywalks), an unforeseen and catastrophic occurrence (the WTC, the Schoharie bridge), and poor maintenance (the West Side Highway).
We can’t be 100% protected from unforeseen disasters – natural or man-made – but as far as design and maintenance, we should be OK in NYC.
(edited and corrected – icot)