Near the beginning, when Batman returns to the Batcave, Alfred is able to successfully convince Batman, who is in the middle of a case, to eat and to go to bed. It's really sweet to see Batman is willing to listen to Alfred despite being a workaholic.
Superman trying to talk a man out of committing suicide, telling him that "everybody matters", and that "you're stronger than you think you are". Sure, it was actually Metallo, and a trap, but it's still a truly heartwarming moment.
If anything it is a scene that didn't make it into the All-Star Superman from the comic, where Superman uses those same words to save a suicidal teenager girl.
Once Superman is hit with the kryptonite bullet, a huge crowd of people gather outside the police lines. No clicking cameras, no reporters, just as many people from Metropolis as can come to see if Superman's going to be all right. Once they succeed in withdrawing the bullet, the whole crowd goes from dead silence to cheering. The people of Metropolis really love their superhero.
Martian Manhunter's secret identity is blown when Ma'lefa'ak poisons him and sets him on fire. His human friends/co-workers rush to try and put him out, still calling him 'John' and 'buddy'.
Such efforts involve one getting up close to douse the screaming, 6ft+ green guy wreathed in flames, with a tiny fire extinguisher, and another crash tackling him with a blanket to try to smother the fire. Considering they just found out who he really was less than a minute ago, but don't even blink, it's really pretty sweet.
At the end, Batman decides to leave the League. Superman points out as he is preparing a teleporter that Batman didn't make a failsafe against himself going bad. Batman simply says, "I do have a plan. It's called the Justice League." While he may be paranoid and a bit hard to get along with, the Bat does trust his teammates with taking him down at least.
* Even though Batman's contingency plans nearly killed the entire League, Superman still trusts him with a kryptonite bullet, just in case Superman should ever go rogue. Superman understands why, even if he doesn't approve.