The ending, where Bowser, while nursing his wounds after being beaten by the Mario Bros. gets a gift from his enemies: A cake◊ with little figures of Mario, Luigi and Peach and Bowser's face right in the middle.
Even more so in that he's always wanted Peach to make one for him ever since Super Mario 64 back in 1996.
Starlow being the one to deliver it is also heartwarming, considering the Odd Friendship of sorts she and Bowser had developed throughout the game.
In Bowser's "memory banks", after failing to repel the Bros., the synapse running the place takes the shape of a pixelated Peach for communication purposes. The synapse says the shape is based on "the host's most carefully preserved memory".
Likewise, using copies of Mario and Luigi as his defense against intrusion into Memory Banks. Shows some respect that rather than following his ego, and having a fake Bowser to fight there, or even an army of his minions, he has deep seated enough respect for the Bros' strength that his mind chose THEM as his defense.
This theme (known as "Have a Nice Talk"). It's played whenever Bowser's friends are around (Broque Monsieur, Private Goomp, Sergeant Guy, Corporal Paraplonk). Even though he may be a villain, he does have friends who help and support him, which makes it all the more heartwarming.
Bowser and his minions. Specifically the ones Bowser rescues from the cages. There was this odd sense of... almost family going on between them, with Bowser being the classic gruff-but-devoted Team Dad. After viewing Bowser as a Jerkass tyrant for years and years of games, it's both odd and touching to see that some of his minions genuinely like him and want to serve him.
Particular mention should go to the part after he rescues the Goombas and gets Goomba Storm, and a Fawfulcopter shows up and Fawful taunts him by showing him various minions in trouble. You can actually see his expression changing from neutral to pissed off as he sees his minions being captured.