Batman's reaction to Superman telling him that he and Lois want Bruce as their child's godfather. The lead-up to it is pretty adorable, too.
Harley Quinn telling Green Arrow that she understands the Joker was a horrible person, and that she knew he was wrong for her. But she says that no matter how much he hurt her, losing him would hurt more. Ollie says that that describes three of the last four women he's been with. Aww...
Captain Cold telling Flash that some heroes and innocents weren't the only ones effected by the destruction of Metropolis, complete with a panel of various villains in a bar having a drink for their own who were killed. They may not agree sometimes, but when they show respect, can't help but feel a bit warmed.
There's surprisingly one between the Joker and Harleen after they fight. She initially mistakes him for an imposter (since the actual Joker was killed years ago in her timeline), though she notices that he moves, acts, and speaks in the exact same manner as he does. Joker follows finding this out up with an extended hand and this exchange.
Harleen: I feel... like myself again... Joker's dead, but... You're...
Insurgency Batman's reaction to the heroic Superman's intended response to the final battle. Particularly as how before he says it, he is just sitting in the background of the scene clearly struggling with his emotions.
Batman: I realize this isn't entirely accurate. But it's good to have you back.
Though her reasoning is twisted, the idea that Catwoman would join the Regime so that she could protect Batman by misleading Superman's attempts to find him in the hope they could be together eventually is rather touching. Heck, though it doesn't work, she even states the reason she agreed to go after him and Green Arrow with Nightwing was so she could convince him to leave with her and start a new life together where Superman would never find them.
In the comics, she was the one who went to comfort both him and Alfred after Superman informed her of Dick's death.
If there was any doubt Insurgency Lex Luthor is a good guy, then him saving Harley Quinn from the Joker and then comforting her after she realizes that she had fallen for him again should dispel all doubts.
In Green Arrow's Classic ending, he travels to the alternate Star City to find a memorial built in Alternate Green Arrow's Memory and that Red Arrow, a.k.a. Speedy, is carrying on the legacy, protecting the streets.
It's just a tiny bit sweet that Oliver carries around a picture of Black Canary, as revealed by the story mode.
The fact that before The Flash gets put into the prison car, he looks back to Green Arrow and gets a nod that causes him to smile. Just the simple fact that seeing the alternate version of a dear departed friend was enough to do so really hits home how close they were.
Also a bit of a Tear Jerker, when Cyborg pays his respects to the Insurgency Lex Luthor by visiting his grave/memorial in the ending. He places the central piece of Luthor's power armor against the tombstone before he leaves, visibly saddened by his death. Even after Cyborg's first interaction with him was the fight in the Insurgency's base, he's still among those that recognize how different this Luthor is from the normal universe's Luthor.
What makes this especially sad as well as heartwarming are the last words Cyborg has with Luthor.
Cyborg:Lex Luthor risking his life to save Batman. I wanna believe it...
When Insurgency Batman decides to send all the main universe heroes back to their universe to save them from Regime Superman's wrath, Wonder Woman refuses to go through with idea as she doesn't want Insurgency Luthor's Heroic Sacrifice to be in vain. It just goes to show how much more heroic he is compared to his main universe counterpart.
Cyborg early on acknowledges the reason that there is only himself, Raven and Nightwing is that most of the other Titans died in Metropolis five years ago. his victory speech after beating Slade is as quoted "I wish the other Titans could see this"
Batman telling Damian Wayne that Dick Grayson was his son, and that, by killing him, Damian is no longer his son and dead to him Bruce and Dick were always close, but this scene emphasizes it even more.
A relatively short, low-key example, but Lex Luthor and Deathstroke bonding on a rooftop.
The scene where Alt!Superman goes to Alt!Lex to have him build a scanner to find the dimension hoppers. While we know that Superman has become incredibly corrupt and Lex is plotting against him with Batman, it's rather touching to see the tyrant who enslaved the world have a friendly conversation with his best friend. Hell, Luthor seems rather genuine with his offer to have dinner and seems rather disheartened after Superman leaves. Deep down, he may still see Superman as his friend.
In the same conversation, Superman smiles when he considers the possibility that the other universe may have a Lois Lane - evidence that even beneath his hardened, cynical outlook on life, Clark is still in there.
Solomon Grundy's S.T.A.R. Labs storyline. Unlike the other normally villainous characters who have predictably villainous goals in their S.T.A.R. Labs storylines, Grundy wants to rescue his friend Birdnose (Hawkgirl).
Aquaman's rejection of the Regime's treaty. Until moments later when Regime!Aquaman reveals himself, Aquaman had no idea as to whether he was in a parallel universe or an altered timeline; it was this very reason why he went to Atlantis (to find out which) and he'd been successfully maintaining an "in the know" ruse until that point. Ramifications be damned, neither time nor space would prevent Aquaman from standing up for Atlantis and helping them resist surface oppression.
After Regime!Superman kills Regime!Shazam, they tell Regime!Grundy to take the body outside. Regime!Grundy then says...
Regime!Grundy: Grundy dig hole. Grundy bury.
At the end of the Story Mode, when Insurgency!Batman gives Superman the obligatory "You go off the rails like your counterpart did I will hunt you down," speech Superman (totally unoffended) tells him that he will have to get in line. While Clark may worry about getting pushed to the breaking point he is entirely confident that his friends will not follow him into any abyss.