Shifu leads Po to the Sacred Pool of Tears. Remember, until that morning, Shifu largely treated Po as an intruder who had no place in his world. Now at that moment, Po realizes that the Master has just led him to the holiest place of all of kung fur tradition with the red panda asking "Do you want to learn kung fu?" When Po answers "Yeah! ...OKAY!" with all his heart, you can't help but tear up with Po when Shifu responds, "Then I am your master!" to show that he knows that the Panda is not a worthless failure, but someone whom that teacher has faith in at long last.
Shifu: (deadpan) "Don't cry."
Po: "Okay." (sniff)
And that all pays off when Shifu and Po fight over the dumpling, midway through, Shifu pauses with a look of wonder at Po moving like he was trained to fight all his life and realizes that the giant panda is the Dragon Warrior after all.
"I'm not hungry."
The dinner scene where the Furious Five, although still resentful of being upstaged by Po at the choosing ceremony but have grown to respect his tenacity, all finally begin to befriend the affable panda.
Except for Tigress, who stoically eats her tiny plate of tofu. She doesn't really accept him until the very end of the movie, in which she is the first to respectfully bow and declare him a master of kung fu.
Viper, on the other hand, hides any resentment on her part very well, being the only member of the Five to treat Po with unconditional kindness from the moment she met him. Even showing concern for his well being when he's not on camera.
Viper is the nicest to Po because, as the only one in her family born without venom or fangs, she knows exactly what being an outsider feels like.
When the Five are evacuating the villagers, a little bunny child is walking around Master Monkey's legs, obviously lost and confused. Monkey gently picks it up, holds it close, and says, "Come little one, let's find your mama." It's small, but it makes the warm and fuzzy feelings come in droves. Made even more so by watching Secrets Of The Furious Five, in which the five overcome various obstacles and Monkey's flaw is revealed to be lack of compassion.
The scenes of kitten Tai Lung when he was first being raised and trained by Shifu were absolutely, undeniably adorable, enough to make a heart of stone melt. (Which only made Shifu's flashback to him leaping in the air for a hug, just before adult Tai Lung, lost to rage and insanity, was about to smash him to a pulp, all the more of a Mood WhiplashTear Jerker.)
The end credits are a series of these: Po showing the Dragon Scroll to the children of the Valley, Tigress doing her own impersonation of Shifu, which pans over to show Shifu laughing, Po getting an action figure of himself, and the last scene where Shifu and Po share their dumplings next to the sprouting peach tree that Oogway planted before leaving. It's all note perfect.
I'd throw in the music that plays with it, both the traditional Chinese music and the remake of "Kung Fu Fighting".
When Shifu declares that it's time for Po to take upon the Dragon Scroll.
Po: You really believe I'm ready?
Shifu: You are, Po.
Keeping in mind that this is the first time Shifu calls Po by name, instead of just "Panda."
This is a movie with An Aesop about being yourself that actually pulls it off. The whole damn movie's basically one big CMOH.
"To make something special, you just have to believe it's special."
" There is no secret ingredient. It's just you."
The Dragon Scroll is a CMOH as stated numerous times on this page. It's supposed to contain what makes you the Dragon Warrior, the greatest fighter to ever exist in a single scroll. When it's opened... It's blank. Reflective. Po realizes what this means later on. It's you. YOU are the only person who can make yourself special. There's no special training, there's nothing you can do but be yourself. Only you can make yourself awesome and the sooner you realize that the better.
When Tigress goes off to fight Tai Lung herself, and is followed by the other Furious Five. It just shows how close they are with each other.
Tigress: Don't try to stop me!
Viper: We're not trying to stop you, we're going with you!
Monkey: *Thumbs up, smiling*
The scene with Po and Oogway at the peach tree is pretty touching, especially how it starts with Po mortified that he's eating sacred peaches. After some inspirational words, Oogway taps the tree, knocking a peach into Po's hand.
Everyone in the village cheering for Po after defeating Tai Lung. Especially his father, who after spending the majority of his screen time trying to convince Po to drop his Kung Fu fantasies and take over his noodle shop, proudly declared "that big lovely kung fu warrior" as his son.
Master Shifu smiles and laughs during the dumpling fight. One has the feeling he hasn't enjoyed himself in a long time, likely since Tai Lung turned evil.
The scene where Mr. Ping tells Po how he found him and how much of an impact he has been for him. After with what happened to Shen and Tai Lung and their parents, it's nice to see a father and son with a healthy relationship.
The fact that everyone is afraid of Tigress because she has no idea of her own strength (being a tigress cub among ducks and rabbits), and they won't even play with her. When Shifu comes, he brings a game with him, and later adopts her because no one else was willing to.
Viper and her father smiling at each other (it's significant, alright) after Viper had defeated the gorilla rogue.
I bring up Monkey's backstory, particularly after Oogway saved him from certain death. That Monkey is the only one who uses a staff also becomes heartwarming, considering Oogway uses one too.
Oogway not only shows the obvious trait of compassion in that short, he shows great humility by straightening out a small-town prankster—a problem which most would call too insignificant for a grandmaster's attention.
Master Shifu comes to the restaurant and finds that true perfection he wanted at the banquet is at the informal dinner at Ping's restaurant; where the lonely have a place in a holiday where togetherness is everything. When Shifu turns to leave, feeling he does not belong, Po comes out and tries to persuade him to come in.
Shifu: Oh no, I couldn't. These are your people; this is your family. Po: You're my family too.
Tigress has SEVERAL. Wishing Po a happy holiday with a genuine smile was one, feeding a baby piglet playfully another by saying, "I'm gonna get you!". Considering how much of an anti-social jerk she was in the first movie, these examples only turn the D'awwwww factor up to twelve and begin the Po/Tigress Ship Tease.
That and Tigress reminiscing with the others at the formal party how much she enjoyed the holiday when she was a child. Though she wasn't the only one, the other masters joined in pretty quick.