Haven't read the book, so you're on your own with content, unless someone else on the forums happens to have perused it.
The lower classes occupied themselves with the orgies and the like that were associated with the "notorious" districts of NYC.
Um. You might need a little more detail here (about the setting, not about the orgies). I'm sure that even the most notorious districts of New York didn't have orgies in the streets in 1890s.
Working-class immigrants only gave added headaches to the "slumming" as in slum bashing upper-class ,
This doesn't make much sense to me. Revise.
Vigilantes took it upon themselves to attack the thickly populated , poor districts.
Again, more details are needed. Vigilantes imply people protecting the streets against dangerous criminals. Were the people in these neighborhoods dangerous to anyone? Were the attacks against gay people, or against poor people generally living in areas known for vice crime? etc.