Commissioner Gordon getting the calmest (relatively speaking) retirement party and Passing the Torch to his daughter.
Batman swinging by the orphanage to give his swag to the kids. Awesome Ego aside, he made those kids' nights because freaking Batman showed up and did his thing! And it's obvious Bruce does it because he knows what it's like to be an orphan.
Alfred's Undying Loyalty to Bruce, where he's even willing to go into battle for him and cares for his mental well-being.
How the Barbara and Batman relationship is tackled. Barbara tells Batman that she idolized him from a young age and wanted to be him. Instead of donning the cowl, however, she became an ace detective and martial arts expert at Harvard, before building her way up in the force. She wants to balance Batman with the law so as to take down crime completely, while working with him. Batman eventually admits that they work better as platonic partners, stepping aside the No Yay issues of the ship.
Barbara is remarkably perceptive about Batman's issues. The first time he realizes that he has nothing to do with the bad guys captured, he kinda goes into a fugue state, and you can see Babs noticing and quietly getting everyone to give him some space without drawing attention to it. Same when he's triggered by the word "family".
Dick having a blast running around Wayne Manor, even while Bruce himself has been ignoring him for a week.
When Bruce first lays eyes on Barbara Gordon at the gala, he's instantly smitten with her. His doofy smile is both hilarious and adorable at the same time.
After Dick gets hurt because the Batmobile has no seat-belts, Batman decides to go slowly and to use his arm as one, also declaring he'll put them in when they go back. It's the first thing in the whole movie that isn't self-centered, showing that he's not 100% jerkass. Keep in mind, he took Dick along as 110% expendable, and yet is caring about his safety.
Not quite the first: It's a small moment that may be lost in a Funny Moment, but Batman is sincerely apologetic after accidentally dropkicking Alfred into the piano and rushes over to see if he's okay.
Batman slowly starting to enjoy working with a partner during the mission to steal the Phantom Zone key. By the time they get out, he's purely happy and excited for a couple minutes before remembering his shtick.
Right after Joker has released an army of otherworldly villains from the Phantom Zone, and Batman and Robin are stuck in Arkham Asylum Dick is understandably terrified. He asks Batman if he's ever been scared, and though Batman denies it adamantly he hears Dick crying softly through the walls and comforts Dick by telling him that Bruce Wayne is someone who gets scared. It's the first fatherly thing he does completely willingly. He then tells Dick:
Batman: Bruno told me once that the only way to get out of a down moment is to start boxin'! And by 'boxing' he meant beatboxing! *the two lift their spirits by improv beatboxing together*
Robin: *completely cheered up* Oh my gosh! This does make me feel better!
Though it was the wrong thing to do, Batman does Shoo the Dog to send his "family" to safety and to put them by a taco stand so that they can be fed when he sees their selfie is similar to the portrait of him and his parents. He considers Robin, Barbara and Alfred as his family.
'Puter overriding Batman's orders to take Robin, Barbara, and Alfred to Bludhaven so that they can all go back and help him.
Batman finally accepting Robin, Barbara, and Alfred's help, and recruiting his rogues gallery to help him. He even designs customized Bat-signals for each and every one of them!
Batman convinces the Joker to help save Gotham at the end by admitting that the Joker is important to him too (in a weird frienemy kind of way), which is all the Joker really wanted to hear. The Joker is overjoyed.
Then once the city is pulled back together and the day is saved, Batman and Joker have an oddly tender moment in front of the rising sun... wherein they declare their mutual hatred for each other. It's as funny as it is bizarrely heartwarming.
Batman: I'm just gonna come right out and say it. I hate you, Joker.
Joker: *GASPS* I hate you too!
Batman: I hate you more.
Joker: *holding back happy tears* I hate you most.
Batman: I'll hate you forever. *smiles*
In most other media, Dick Grayson (and the other Robins) are Bruce Wayne's "wards" and actual adoptions take place a long time later (if ever). Here, Dick is immediately adopted by Bruce (albeit by accident), and then recruited into crime-fighting because of his usefulness. The fact that Robin constantly calls Batman variants of 'Dad' is as sweet as it is hilarious.
Robin also calling Alfred "grandpa" might be even sweeter. With Robin being Batman's adopted son and Alfred being Batman's father figure after his parents died, this makes sense.
Batman revealing to Robin at the end that he's Bruce Wayne, and finally giving him a hug. Dick sheds a tear, and his dad lifts up his goggles to let it fall.
Robin: Padre, please...
Batman: Don't call me 'Padre'. [...] call me *Batman removes his cowl* Dads.
Batman's fatherly consolement to Dick before he leaves for the Phantom Zone is a culmination of all the character development leading up to this point, which incidentally blows a lot of other incarnations of Batman's flawed views of life out of the water.
The last shot before the credits is Bruce hanging Dick's selfie of him and his new Bat-Family right next to a selfie Bruce took as a child with his own parents. The general layout is the same in both photos with the son in the foreground and the rest of the family standing together behind him.
The scene leading up to this is equally adorable, all set to Alex Aiono's cover of "Man In the Mirror". Bruce finally gets to have a lobster dinner with his new family!
Batman's narration after the shot is also pretty sweet considering how he usually is:
Batman: White. All important movies end with a white screen.
Odd as the scenario may be, it's still sweet how all of the Joker's villainous friends are genuinely supportive of him during his relationship problems with Batman. Especially Harley, who is seen smiling in the background when Batman finally admits that he is his enemy.
Despite stabbing them all in the back earlier in the movie, it is nice to see the Joker allowing to rest of the Rogues Gallery to walk away with him. Some of them were cheering him on due to the fact that he got Batman to confess to him.
Joker: Let's go, gang!
Other Rogues Gallery members: Joker! Joker! Joker!
The fact that Joker and Harley aren't in an abusive relationship but are BFFs, Harley supporting Joker when he's depressed and Joker not being manipulative towards Harley. It's also really sweet how Harley calls Joker by cute nicknames like "sugarplum" and Joker in turn calls her "girl-buddy".
