The last movie ended with the Furious Five calling Po "Master", hinting at respect and distance from the Dragon Warrior. But the movie starts with them being so close that all five (even Tigress) having fun with Po betting he can fit 40 bean buns into his mouth. Becomes extra heartwarming since "hanging out" with the Furious Five had been his dream for years.
Tigress reaction to that is telling Po that "his training paid off". Compare to the previous movie, when she was angry because she believed he didn't take kung-fu seriously enough. It shows both her relationship having improved, and Tigress herself being more at peace.
This little exchange at the end of the film:
Po: I know who I am.
Ping: You do?
Po: I'm your son.
Also counts as a Meaningful Echo from earlier in the film, where Po asked the question, and Mr. Ping gave the same answer. Becomes even more heartwarming since Po didn't reply when Mr. Ping asked Po about their relationship before Po leaves.
Po: The hardcore can't understand. Viper: Tigress, no! (Tigress lunges at Po and hugs him, to everyone's shock) Tigress: The hardcore do understand... but I can't watch my friend be killed.
Any of the Po/Tigress moments could qualify, especially in the final half.
Several times in the movie, Po gets thrown or falls over. Most times, Tigress immediately picks him up or catches him without even thinking about it. She's come a long way.
There's that private nighttime conversation on the boat. Imagine, Tigress, Po's Resenter in the first film, has grown to become the panda's best friend and confidante of the Five, and maybe the seeds have been laid for something more.
Even more subtly in the film's Super Bowl ad, when you notice that when Po makes his fist excuse, Tigress is smiling with a warm understanding at her friend's effort.
The scene at the end where Po swims up to Tigress at the climax of the film after everyone is hit by Shen's cannon. He whispers her name, holds her hand, and even looks at Shen with a very angry tone. Then, when he pushes her out of harm's way, her hand is still out as if she still wants him to hold it.
Remember, Tigress said that she couldn't feel anything physically because of her Training from Hell she endures (by punching ironwood trees for 20 years). To feel Po's paws just... it just adds more depth to their relationship.
Just the fact that one of the film's producers, specifically, Guillermo del Toro, came out and said that his own opinion was that Po and Tigress's moments are really meant to hint at romance and that he played a part in adding them.
The scenes with baby Po. Po starts off as a handful, but Mr. Ping's patience and love pays off and we see Po grow up to be, well, a goofball but a caring and good-hearted one.
A rather subtle one: In the beginning of the first film, Mr. Ping mentions how he'd always wanted to learn how to make tofu. In the sequel, we see that he has learned to make it and now serves it alongside his noodle soup. In short, Po's success has inspired him to pursue his own dream.
Another subtle one: At the end, Po suggests that he and Mr. Ping cook together, which was the subject of Ping's happy dream in the Holiday Special.
Po offering Shen, the one who slaughtered his own people, a Last-Second Chance. Even though Shen doesn't take it, it still shows a great deal of compassion on Po's part to try and redeem the murderer who orphaned him.
The montage just after Po remembers the probable death of his mother, then to realize things worked out well enough with the love of Mr. Ping creating a home where he was not only loved, but it is in a place where he achieved his most cherished dreams and found his dearest friends, with the last scene of the montage being of Mr. Ping and Baby Po together in his noodle shop.
A small one, but Po kissing a bunny toddler on the forehead was quite cute.
Po and Shifu at the end:
Shifu: At last, you have achieved inner peace...and at such a young age.
Po: I had a good teacher.
Shifu's instinct to be Papa Wolf at the first sign of Po in trouble. It just shows that this man has a lot of love to give, since a literal army could not stop him from reaching his surrogate son.
Towards the end after defeating Lord Shen when the remains of his ship, fireworks erupted. It then showed a vague shape of a peacock resembling Lord Shen. It then pans to the Soothsayer, smiling. Maybe Lord Shen did find his peace.
"My son is alive."
Ping's adorable flashback to when he first adopted Po, accentuated beautiful by the lightly stringing music. Heck, Ping in general, as he is such a devoted father.
The scene with Baby Po you can hear him say his first word. "Da-Da"
Mr Ping: And from that day on,both my soup and my life has been that much sweeter.
What does Ping do when he finds a crying panda cub in the empty basket that was supposed to have his order of radishes? Leads Po in, bathes him, clothes him, and feeds him (repeatedly) while waiting for Po's parents to come looking for him. And when noone shows up for the child? Ping immediately decides to adopt the child as his own without a second thought.
The Furious Five all glomping Po after he saves the day in a particularly awesome way. And remember that they thought Po was dead before the final battle began. They're just so happy to see him.
When a couple of indignant customers keep pestering him about where the Dragon Warrior is, Mr. Ping snaps, and goes on a rant about how worried he is about his son. Right when he seems on the verge of crying, Po makes his return. The welcome back hug he gives is maximum heartwarming.
Lord Shen letting the Soothsayer go. For all his evil, he just lets her leave, no strings attached. And her last words to the man are that she wishes him to find happiness.
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.
During the "I Am Po" moment, while a some of his memories are scenes from the first film, Ping dominates his memories.
Also noteworthy is how all his memories are either from the first film or from the past, apart from one that happened recently: Tigress hugging him.
The short starts with Po finding out that his dad accidentally gave away his Furious Five action figures, and he frantically goes out to search for them. In the end, he finds the bunny child that got them and ends up watching proudly as the child trains kung fu with them, just like he did. When the (real) Furious Five arrives and asks Po if he found his figures, he replies that they're right where they need to be and besides, he "has the real thing", before putting his arms around the Five and walking off.'
The Fact that the Five treat the situation seriously, asking Po if he found his "dolls" and not making fun of the situation in the slightest.
Viper and her Father's relationship has turned around since we last saw them in flashback; He tells her that he is already proud of her. Sadly, this makes Tigress kinda jealous.