The scene where Robin leaves Batman is kind of touching. It really shows how much they trust each other.
In a probably twisted way, Batman contemplates why he should give the cure to the Joker, when the Joker stabs Batman, making him drop the cure, dooming himself. Batman admits:
Batman: Do you know something funny? Even after everything you've done... I would have saved you.
This is probably the only continuity where Batman and Mister Freeze actually patch up their differences. For once, Victor gets a relatively happy ending!
Freeze even admits he was wrong and apologizes to Batman. He also apologizes for doubting him as well, and given that he has always blamed others for stuff he did wrong in the past, that is saying something.
You can go and visit Freeze and Nora during the epilogue. The affection he shows toward her is almost creepy, seeing as she's a block of ice, but also very touching.
Returning to the steel mill after Protocol 10 is activated nets you a scene with the Abramovici twins reconciling. Humorously, they want to take it all the way by getting reattached.
Hammer: It is good to see you again, brother.
In Catwoman's DLC, you can have her choose to drop the loot she'd worked so hard to get and go save Batman. It was actually quite touching.
Especially if you've unlocked Catwoman's interview tapes. Strange tried to undermine Catwoman's feelings for Batman, saying her hesitance to accept a man's help keeps her from an actual relationship with the Dark Knight. To see her pass up the loot to help him in light of that adds so much to that scene.
Even further: if you direct Catwoman to take the loot and run, you see a Non-Standard Game Over in which Batman dies under that rubble, Strange's plan succeeds, and Joker escapes with the cure and takes over Gotham. Catwoman's rescue is the only reason that Batman survived to save the day.
A small one, but sweet nonetheless. In Aaron Cash's office at Arkham Asylum, there was a picture of Cash, his wife, and his son. In his office at the church, there's another picture of them with a baby added to the family.
The Joker singing "Only You (And You Alone)" in the credits, seemingly recognizing the irony, yet playing it straight at the same time. It's really bizarre having a touch of empathy for the mass-murdering lunatic.
The Joker's insightful, and surprisingly sympathetic message about how lonely Batman's life makes him. It's one of the few rare glimmers that there was ever a person in there.
Visiting The Mad Hatter as Catwoman any time after you've beaten him. Jervis asks Selina if she's "Alice", which prompts her to comment to herself about how "Strange really did a number on [him]", and reminds him that she's Catwoman. He continues to ramble on and on about finding "Alice", and Selina offers this somewhat sweet set of words to him:
Catwoman: Listen, I'm going to go find 'Alice' for you, okay? I hear she's with the Cheshire Cat...
Assuming she wasn't mocking him anyway.
If you listen to the chatter of the political prisoners, you'll occasionally hear them trying to reassure and look after each other. It manages to be rather sweet.