Many moments in Milk would qualify, as well as double as Heartwarming Moments. But probably the ultimate example lies when the news is broken that Prop 6 was overwhelmingly defeated. Even knowing the real life truth before seeing it the first time it has brought a tear to this troper's eye every time.
This troper punched the air and cheered- that's how emotionally invested I was in a film despite knowing that it was rooted in real life, and knowing that they would be successful.
All together now: "My name is Harvey Milk... and I want to recruit you."
Doubly awesome when you realize it's probably also a jab at the common claims (read: blatant lies) that homosexuals want to "recruit children."
The funeral scene manages to be this, a Crowning Moment of Heartwarming and Tearjerker as We see the endless line of mourners paying their respects. Milk's famous "without hope, life is not worth living" speech never fails to send chills. Made even more amazing by the fact that the line of mourners wasn't special effects and real footage was used.
When Milk gets his first death threat, he pins it up on the fridge, since he believes that hiding it away will only make it bigger. When it's in plain sight, it can't hurt him.
Before making a big speech, Harvey gets an anonymous threat claiming that he will be shot as soon as he speaks into the microphone. Milk goes up onstage and delivers a beautiful speech, completely fearless. Some might not have gone up onstage, some would have delivered a rushed speech, but Harvey Milk did exactly what he intended do to and made a huge impact on the crowd.
Despite the obvious bias of the audiences they spoke to, Milk's debates against Briggs are awesome to watch. Briggs' arguments are clearly flawed and intended to incite homophobia, but Milk just rips into them and points out why he's wrong. "How do you teach homosexuality? Is that like French?"
The most awesome thing of all? Harvey Milk was, of course, a real person. All the achievements you see onscreen weren't made up, this was a real man, a real human being who fought for what he believed in. Truly an inspiration to us all.