I never held up any particular scene as an accurate depiction of events. What I think is fine about the film is the creation of atmosphere that truly existed in NYC at the time - particularly relating to the Draft Riots and evils of Tammany Hall and the slums of 5 Points. That is accurately portrayed if my book of mug shots from the 19th century is anything to go on. Also, I live in NYC as has my family since mid-19th century so I have a slightly atavistic attitude towards both the movie and those times.
And you're not the one of the ones I'm talking about. And I'll certainly concede that the movie looks great.