Near the beginning, after retrieving loot from a band of thieves, Aladdin doesn't hesitate to toss almost all of it into the streets of Agrabah for the needy and poverty-ridden, most likely remembering his own life prior to the first movie.
"Abu! We're not the ones who need this money."
When Aladdin arrives at Jasmine's place, Rajah is threatening towards him. It looks like he still isn't friendly towards him despite saving, him, his owner, and the Sultan from Jafar and pounces him... only to lick him affectionately, showing he has warmed up to him.
When Genie returns to Agrabah, he almost immediately launches into a musical number about his trip around the world... and how much he missed Aladdin and the others during it. Even the line right before the start of the song:
Genie: But Agrabah has something that no other place in the world has... YOU GUYS!
Despite being free and being able to be anywhere he wants, Genie chooses to return to Agrabah to be with his former master Aladdin, making it clear that he regards Aladdin as a friend and seeing the world by himself just wasn't the same as staying with the people he cares for.
Now that I'm home / Home again it's clear / All I've ever wanted / Seems to be right here
When Jasmine is angry at Aladdin for keeping Iago's return a secret from her, Iago reveals that Aladdin helped him because Iago saved his life and (with the help of Genie's magic) convinces Jasmine to forgive him.
After the song, Jasmine softly scratches Iago under his beak, an affectionate gesture.
Iago hears Aladdin and Jasmine talking after Jafar returns, with Aladdin revealing he believes that Iago has changed and Jasmine decides to give Iago a chance, even saying to him that she was wrong about him and giving him a kiss. It's enough that Iago nearly comes clean immediately, only for Jafar to intimidate him into silence.
While Genie saving Aladdin from the executioner's block and carrying him away is pretty heartwarming in itself, it becomes even more so when you contrast it to him saving Aladdin from drowning in the first movie. This time, Genie could just go and do it, without having to consider whether Aladdin actually makes a wish or not.
Aladdin: Thanks for saving me!
Genie: Ah, Al, you know I had to! That no-head look is just not you!
The way Jasmine elatedly cries out Aladdin's name when she sees that Genie made it in time to save him. Also, Abu joining in as they embrace.
During the final climax, Iago has been beaten down to near certain death by Jafar. Now apparently a goner and with nothing to lose or gain from serving either side anymore, he chooses to save Aladdin's group and destroys Jafar's lamp in what strength he has left. Doubles after he gets better after all.
Iago originally intended to befriend Aladdin as a way to get back into power. However, he ends up genuinely liking Aladdin after he sticks up for Iago and is unable to go through with Jafar's revenge plans, choosing Aladdin over Jafar. As a result, he becomes Aladdin's second pet.
