The reparation of the relationship between Alfred and Bruce. After the former is almost killed by Bane, Bruce finally begins to realize how selfish and thoughtless his actions have been and begins to warm up to the idea of having help.
On a similar note, Batman and Gordon's relationship as well. The two are never really on good terms until Firefly holds the bridge for ransom. By the end of things, both of them realize how invaluable an ally the other was during the event.
A short but sweet one is Alfred wishing Bruce a Merry Christmas over their Comm-link and Bruce returning the notion. Borderline Tear Jerker because of the solemn tone of the conversation since Bruce couldn't make it home for Christmas.
Even more heartwarming is the post-storyline when Alfred tells Bruce that he's been keeping Christmas dinner warm for him, knowing he'll be coming home right after wrapping up some loose ends.
Additionally, when Bruce suggests that Alfred get some sleep, Alfred responds "not until you're back safe and sound", and says that they can have Christmas Dinner for Breakfast.
Helping Barbara take down Penguin's arms caches. She's ecstatic to be working with this symbol of justice she believes in so readily.
In a twisted sort of way, Bane hoping Batman finds "peace in death that [he] did not find in life" as the former is trying to kill the latter. And he says it without an ounce of mockery.
Joker and Harleen get a moment that is kind of sweet in a twisted way and rather ambiguous given how it's unclear whether Joker genuinely means it (both of which is as usual for them); when Joker asks if her friends call her "Harley", she says she doesn't have many friends. Joker smiles at her and says "Well, you've got one now."
In the Initiation DLC, Kirigi is shown going from extremely brutal and racist toward the American Bruce Wayne, to grudging respect, to, upon his defeating Shiva, actually warmly welcoming him to train with him...if you get all 15 medals. After all of the work, it seems to mean a lot to Bruce, even though he says nothing.
When rounding up the escaped Blackgate convicts, one of them begs Batman not to send him back because the guards are worse than the prisoners. Batman knocks him out and sends him back anyway, but not before he assures the prisoner that things are going to change and tells Gordon to send a police officer who's trustworthy to come collect him.
It's possible to talk to cops that have been rescued from random crimes, and while a lot of them seem to indicate that they're only letting you walk away because you saved them, there's a chance that the response will be an honestly grateful comment that the department is wrong about you.
Further continued in Cold, Cold Heart where cops will be grateful to Batman for thawing them out of their frozen cocoons with the XE Suit.
After spending the first half of the DLC thinking Mister Freeze is a cold, heartless monster, Batman ends it by rescuing both Nora and Victor and promising him that Boyle will face the law for his crimes.
Batman: I'm sorry, Victor. I can't grant you peace. ...But I can give you justice.
Over the credits, the news report states that not only have Boyle and the Penguin been arrested, but the corrupt mayor of Gotham, Hamilton Hill, has resigned after facing "anonymous" allegations of ties to the Maroni crime family... which means that James Gordon is now on his way to becoming Police Commissioner.