Boss Tweed is supremely disappointed that Bill Cutting has just killed Monk McGinn, the Irish sheriff. "You don't know what you've done to yourself." Daniel Day-Lewis then scares the ever-loving crap out of everyone when he taps that knife against his glass eye.
The authentic tunes from the era they got on the soundtrack were awesome as well, such as "New York Girls" and "Paddy's Lament".
Even if it's anachronistic for the time period, nothing sets the nightmarish tone for the battle to come quite like "Shimmy She Wobble."
The Bishop smacking McGloin across the head after he complains about there being a "nigger in the church" is awesome, and hilarious as well. He's such a Jerk Ass that even a Bishop wants to violently shut him up.
It's a minor thing, and words don't really do it justice, but the two occasions when Bill responds to a cheering crowd with a bored royal wave have always been stand-out moments. The fact that he can make a gesture which is so arrogant and dismissive of the adulation (and even look irritated by the tedium of it,) and actually not come across as a pompous Smug Snake in any way is quite remarkable. May be a Moment of Awesome for the actor rather than the character, but either way, it's awesome.