The quiet moment with the combined pair of superteams, in which there's reconciliation, reflection, and in a tearjerking moment, Hal Jordan and Barry Allen (both deceased at the time of the series) talk about missing the opportunity to have a picnic with their wives together, topped off with a talk between Superman and Captain America in which they reveal their private fears; Superman worries the JLA is doing too much for mankind, stifling its growth, while Cap worries that the Avengers aren't doing enough. They acknowledge just before returning to their own respective dimensions that it doesn't matter in the end, so long as they fight the good fight.
Cap loaning his shield to Superman.
Superman: I'm... I'm honored, Captain. I'll do my best to wield it well.
Keep in mind Superman's motto: "Truth, Justice and the American Way."
Green Arrow, thinking Hawkeye has been killed, takes his arrows and vows to make each one count. Throughout the series, their massive egos had clashed over who was the better archer.
During the third issue, Hawkeye and Green Arrow sniped at each other◊, with Black Canary rolling her eyes and say, "Oh, not this again" with a grin on her face. When Superman and Captain America come to blows, both of them are aghast and tell them to chill out. The strong indication is that their fierce rivalry is just part of a deeper friendship. Also an excuse to show off their marksmanship to everyone else watching. (Even more charming, Elongated Man is all too happy to help them show off.)
Speaking of which, Hawkeye is also now the only Marvel character to have been officially inducted into the Justice League of America.
During the final battle with the various enemies gathered by Krona against the two joined teams. After Hawkeye apparently died in action, Wonder Woman ordered the rest of the heroes to press the attack, while she would take up the rear and fight off anything that might attack them from behind. As she prepared to face Surtur, her mother Hippolyta (the Golden Age Wonder Woman) and She-Hulk announce that they will fight at Diana's side. Shulkie's comment was especially in-character (doubling as CMoF):
She-Hulk: Hey, Star-shorts! Thought I might hang, in case you get bored. We could talk girl talk— you know, ass-kicking, name-taking, like that.
Wonder Woman (Hippolyta): Aye, and I stand with you as well, daughter.
Wonder Woman (Diana): I... am honored. And I thank you. Forward, then— For the glory of Gaea!
Even more Heartwarming in that Hippolyta was dead at the time, giving Wonder Woman one last time to be with her mother.
After the final battle, Superman discovers that he can't lift Thor's hammer anymore. Thor explains that Odin temporarily suspended the enchantment in order to let Superman wield it. But then he adds this:
Thor: Perhaps it was but briefly... but it was in good hands.
While it would seem that someone like Superman would easily fall under the "if he be worthy" clause of Mjolnir's enchantment, being worthy of a warrior god's mantle requires a willingness to kill, when circumstances necessitate it. Superman, however, sticks to Thou Shalt Not Kill.
Barry Allen and Hal Jordan, commenting that the Flash and Green Lantern legacies are in good hands with Wally West and Kyle Rayner. This line from Barry is what really sells the deal (or it did, before the concept of Comic Book Death got so cheapened):
"Maybe it's not so bad to die. Not if you leave a legacy, if you know someone'll still be fighting for what you believed in."
Vision giving up the last of his strength to help Superman fight Radioactive Man and Solaar.
When Superman mourns Vision later, Thor points out that he's been repaired after sustaining far worse damage before. He adds that Vision would have given more if he could.
Seeing Kismet and Eternity, the physical embodiment's of the DC and Marvel universes respectively, fall in love is a literal heartwarming moment between the two universes. Seeing them pulled apart is equally heartbreaking.
On a meta level, this symbolizes the respect and friendship that DC and Marvel hold for each other, regardless of their rivalries. After all, if the two big names in superhero comics didn't love each other, crossovers like this could never exist.
A minor one, but the gentle way Wonder Woman offers to prove the Grandmaster is telling the truth with her lasso - and she allows him to retain dignity while doing it by simply wrapping it loosely around his wrist three times.
Another minor moment, when they're making ready to leave the batcave. Captain America takes Batman's remark about Ben Grimm's "rough-edged charm" as an insult. Cap defends Ben by telling Batman that Ben's one of the finest men he knows.
As both worlds are on the verge of merging, Captain America snaps at the Justice League (mainly Green Lantern Hal Jordan). Superman gets angry and defends Hal from the Captain's accusations. True he goes a bit overboard, but his heart was in the right place.
Superman: You have no business criticizing a better man than you'll ever be!
Before returning to their respective universes, Captain America salutes Superman and by extension the rest of the JLA team.
Every hero who has ever been in the Avengers or the Justice League appears in the final battle, including all of the spinoff teams. Yes, even the Great Lakes Avengers and Justice League Antarctica. They may be the laughingstock of their profession, but they join the fight to save their worlds, as true heroes.
Iron Man discovers just how special a Mother Box is - not the power they have, but their personality. Mother Boxes generally are walking Crowning Heartwarming of Awesome-s, but now a Marvel character gets to find out.
Iron Man: I don't... don't think it's a "gadget", Cap. She's... speaking to me... through my armor, through my heart. She's called a Mother Box... and she and I... we can...
The twin forewords to the trade paperback collection, written by Stan Lee and the late Julius Schwartz. The pride the two old men of comics have that their heroes are still going strong after four decades is inspiring.