In this interview by Sarah Schmidt, Nagle explains how bad it actually was:
"Going back 100, 150 years, American cities were disgusting -- and New York City was notorious as the filthiest and stinkiest. We were a laughingstock. The rumor goes that sailors could smell the city six miles out to sea."
Corruption was the real problem, because the street cleaning funds were being embezzled by politicians.
Nagles says that the garbage was so deep that "...the streets were layered in this sludge of manure, rotting vegetables, ash, broken up furniture, debris of all kind."