Kumiko, on Miyagi and Yukie's impromptu tea ceremony: "They're re-kindling their relationship, Daniel-san"
And later Kumiko performs the same tea ceremony for Daniel.
Daniel begs Miyagi to let him come along when he goes to Okinawa to visit his dying father, on the grounds that, "When I need you, you're always there for me."
Later in the same movie, Daniel helps Miyagi mourn the loss of his father.
After the typhoon in which Sato learns the true heroism of Miyagi and Daniel, Sato comes with a work crew to rebuild the village and asks for Miyagi's forgiveness for all the trouble he caused. To that, Miyagi warmly responds, "Oh Sato, nothing to forgive."
During the typhoon, Daniel saved a little girl who got caught in the local tower during a typhoon which triggered both Sato's Heel-Face Turn and his rejection of Chozen. Later, in a local celebration Daniel attempts to follow the little girl as she perfoms a traditional dance...
Daniel: If not for you, I'd have made a lot more mistakes.
Girl: If not for you, I no be here!
During Daniel and Chozen's final fight, and it looks like Daniel is gonna lose. Cue to Miyagi and the rest of the audience using little Japanese toy tambourines to show Daniel they support him. Daniel goes into My Name Is Inigo Montoya mode and wins.
Mr. Miyagi's use of the drum wasn't just to show support, it was to remind Daniel of the drum technique he had taught him earlier, which Daniel promptly used to beat down Chozen. It's still heartwarming when you realize that, by reminding him of such a detail, he is supporting him in a way.
Daniel's birthday celebration at Mr. Miyagi's home in the first film was rife with this, as it showed that Daniel meant much more to Mr. Miyagi than just a student. When he took him to the driveway and said, "choose" the look on Daniel's face was nothing short of amazing.
Daniel(soon afterwards): You know, you're the best friend I've ever had.
Miyagi: You pretty okay too.
While the end of the first movie was pretty heartwarming since Johnny gives Daniel the winning trophy personally. Props go to Miyagi for saving Johnny from Kreese in the second. Even though early on in the first he was the one fighting Johnny.
In the beginning of the second film, Mr. Miyagi has Daniel help him on an extension to the house. When Daniel asks him who it's for, he says a "refugee" from Fresno. He planned to let Daniel stay with him for two months while his mother took a business trip out of town.
A blink-and-you'll-miss-it moment in the third film (which overlaps with Tearjerker). Miyagi takes out a picture of himself and Daniel, who has been drifting away from him lately and has confessed that he feels 'confused.' Miyagi looks at the photo and softly utters two lines:
Miyagi: Hope confusion end soon, Daniel-san. Miyagi heart empty without you.
The ending of the third film, where Daniel hugs Miyagi happily.
On the anniversary of the deaths of Mr Han's wife and son, Dre comforts a crying Mr Han by using bamboo shafts to try to take his mind off the anniversary by going through their forms, that he can eventually heal from the loss. And one of the first things he does is use the bamboo shaft to help Mr Han wipe his eyes.
A promotional interview on Oprah showed that the Smith family took some real quality time together in China. Big brother Trey had prior commitments, so what did Will do? He flew back to California for each of Trey's football games.
The doctor at the tournament, after deciding that Dre is medically unfit to continue, notes to the boy,"You've brought great honor to your family." Regardless of what happened next, Dre can know he's impressed a lot of people that day.