The secret prologue reveals that Yu is dancing in the LMB Festival with the blessing of his parents, despite them being against him pursuing such activities in the original game.
Somewhat undermined by the realization that that means they signed off on it, but couldn't be bothered to actually show up at the festival.
Nanako is already a walking, talking heartwarming moment, but watching her dance alongside her Big Bro is simply adorable.
Everything involving Kanami and Nanako makes you want to hug the person in your immediate vicinity. They are sweet as sugar together in Story Mode.
When Nanako is staying over at Kanami's apartment, Kanami attempts to help her get ready for bed. As she does, Nanako sleepily calls her "Big Sis." Kanami reacts appropriately with an "Oh my goooosh."
This is also something extra special for Kanami as absolutely none of the female members of the Investigation Team are on "Big Sis" levels with Nanako. She treats them as equals, but Kanami becomes someone she looks up to on par with her Big Bro. This is also after Kanami is so blown away by Nanako's dancing talent that she stopped using "-chan" for Nanako and instead started using "-san," which she continues to do for the rest of the game! What does that mean? They respect each other as much as they come to love each other.
For those who played Persona 4 proper, the above scene is also something special for Nanako too. Before, she was completely isolated at home with a workaholic father (Ryotaro) just 1-2 years ago. By the time this game gets rolling, Nanako shares her friendship and trust with Yu, Ryotaro, and the rest of the Investigation Team, and now she's befriending Kanami on top.
In one case Ryotaro (Nanako's father) too has his moment. When Ryotaro calls Kanami on the phone to discuss the missing members of Kanamin Kitchen, he asks the latter to ask Nanako for some privacy. While Kanami is hesitating, Nanako did so without being asked to. Back in Persona 4 proper, Ryotaro was unable to face his role as a parent and neglected Nanako by physically and emotionally fleeing into his work. Here and now, Nanako understands that her father strives to protect Nanako and others, Ryotaro also fully trusts Nanako, and the two are much closer as father and daughter - which both proudly declare as such to Kanami immediately afterwards.
Before starting his first dance in the Story Mode, Yosuke loudly declares that he doesn't care if he's uncool or embarrassing as long as he's got friends who respect him. Watch this scene and then look back at his Shadow Event in Persona 4 and the amounts of Character Development apparent should bring some manly tears to your eyes.
Similarly, Teddie repeatedly tries his everything to encourage the idols to resist the ribbon's mind manipulation and not throw their identity away, even if they're afraid of being hated. He's probably the most passionate of the group about it too, and for good reasons: Throwing his identity away for this exact reason was what kicked off his entire character arc in the original game.
Yukiko and Tomoe bonding over their mutual weirdness.
Shortly before the climax, the fans give Kanami their support. While the game does not shy away from the darker side of the Idol Singer business and the fans' culpability in it, it also shows that there's something beautiful about performing to please the audience, and of the support that grateful fans can give.
Kanami finally letting herself remember Yuko.
The dancing quotes in general - it's quite nice to see everyone supporting and getting along so enthusiastically with each other, especially in the cases of pair-ups like Yosuke and Chie (who in most circumstances are in With Friends Like These... territory). The Suddenly Speaking nature of Yu also lets you see him reciprocate his friends' support, and boy does it show.
Margaret's little speech in the epilogue of Story Mode. Before she sends the player on their way, she tells them not to worry about the Investigation Team — they'll carry on helping others and growing as people. As the game was released near the end of Persona 4's time in the spotlight (and right in the middle of the Persona 5 hype train), the line has a bit of meta-narrative to it: the implication being that the end of an era in the franchise doesn't necessarily mean The Fellowship Has Ended for the characters. No matter what you think of P4's role as a Cash Cow Franchise, it's reassuring to think that they may well stick together in the future, just as their P3 forerunners did.
The overall story of Persona 4 finishing in this game is essentially this for the Investigation Team and Nanako. Back in the main story, everyone had their doubts either through their Shadow Events, or their personal dramas in life, and with no one to talk to. Thanks to both Yu being a understanding listener, and everyone in general working together, they all more or less came to terms with their issues and moved on forward. By the time the story for this game kicked off, they are in a much better position to help others in need. This is most pronounced with Rise, who is even implied to assume a more mature and confident Risette for her comeback with a less childish voice from Ashly Burch.