An early chapter has Team Rocket's Meowth learn Pay Day from a female ninja Meowth. In a later chapter, we learn that this female ninja Meowth is Meowzie, who is the reason why Team Rocket's Meowth learned to act human.
Even better, it means that she's not homeless anymore like she was in the original time line!
Team Rocket acting competently. I'm not quite sure why, but given how much of underdogs they were, it's really nice to see them get victories, see them actually on Ash's level, get acknowledged by the Boss as being hard workers...
Chapter 20 has the birth of Damos, the first new Pokemon that Professor Oak has gotten for himself in a decade, whom he welcomes into the world, and his home, in a particularly touching manner.
Mewtwo's reaction to getting his memories back. It really shows how much Ash got to the guy in canon.
Ash got most of his badges the first time around in the tests of Character. It's kind of heartwarming to see the guy honestly winning matches, instead of, say, getting rewarded for saving the gym from Team Rocket.
Ash learning that his father didn't abandon him by choice.
Ash recognises Dexter as his own person after coming back in time from the beginning, vs. Meowth who treats him as a thing until he becomes a Porygon.
In the second part of the Power of One arc, Ash is ambushed by Hunter J, who orders her Drapion to use Toxic with the intention of killing Ash. Riolu, realising this, throws himself in the way to take the attack for his trainer and friend. He subsequently evolves. When Ash realises this, his new Lucario says the following:
Lucario: As you kept faith with me, so I with you. Go. I'll handle J.
In Johto, when Brock helps the baby Stantler again. Large portions of this arc were written from Stantler's point of view, and the heartwarming factor is almost too much to bear. It's crowning moment is when Stantler chooses to go with Brock rather than stay with the herd.
When Ash visits the school in Violet City, one of the students asks him which of his Pokémon he thinks is the best. Ash, who does not and has never played favourites, lists the individual strengths of each of his Pokémon, and then tells Charizard's story without mentioning that it's about Charizard until the very end. Given that the kids all know how awesome Charizard is, Ash's point about not disregarding any Pokémon as weak and the importance of befriending them is well and truly made.
The end of the Spell of the Unown arc, when Molly learns that the Legendary Beasts and the Eevee she created are now real and then gets her parents back.
Remembering Casey's preference for black and yellow Pokémon, Ash makes plans to give her a Shiny Riolu.
The fact that even though he didn't know Casey well enough to bring back her memories and Pokemon (like he did with the Rockets, Brock, or Misty), he still thinks highly enough of her to think she's worthy of a Riolu (which in-universe is a big deal) is pretty heartwarming as well.
It's not just Ash and company's Pokémon that are True Companions. Meowth showing his support to a bitter Cubone exemplifies that this Team Rocket cell counts too.
After Keldeo transforms into his Resolute Form and uses Secret Sword, Cobalion remarks that he looks just like his father.
Ash managing to rescue Pikachu after the latter was captured by a Dark Ball.
Team Rocket comes across Pikachu's lightning-marked Poké-ball. Their life-long dream of capturing Pikachu is literally within their grasp... and then they choose to give it back to Ash.
A subtle example, but why does Giovanni order Persian to give the Iron-Masked Marauder a stroke? Because if his scheme to capture Celebi had succeeded, Giovanni might never have met Persian. Say what you will about Giovanni, but he does truly care about his partner.
During the mess caused by Ash and co. breaking time we saw a beginner trainer with expensive shoes starting his travel with five empty Ultraballs and a Meowth. Guess who this guy was?
Todd, on his way up a mountain to photograph an Articuno, is surprised by one landing in front of him, curious at his camera. He explains that he just wanted to see its nest at the top of the mountain so he could photograph it, and Articuno flies off. Later, he sees two Articuno flying around one another in a mating dance and realizes that the one Ash saw and the one he saw were not the same Pokemon, he just made the second one aware of the first one's existence. Better yet? He got lots of photos of the mating dance, meaning that for possibly the first time, a Legendaries' mating dance is caught on film. So to sum it up, Todd and Ash accidentally played matchmaker for a legendary pokemon, and then Todd got to witness one of the rarest events in the world. Wow.
After the events of Voice of the Forest, Pikachu is feeling guilty of all the destruction he caused while he was Shadow-fied via Dark Ball, and wonders if he is too powerful for his own and his team's good. Ash's hug and Lucario's reassuring talk say it all about what they think about it, especially since Lucario was going through a similar thought process about not being strong enough.
Later that evening, Pikachu gives his Light Ball back to Ash, telling him only to give it back when his trainer thinks he is safe with it. Ash gives it back the very next morning.
What is the first thing Ash is thinking when he arrives in Olivine City? Not the next gym battle, but the ill Ampharos of the local lighthouse.