After they arrive in Okinawa and see a poster of Sato breaking a log with his bare hand, Daniel asks Miyagi if he could do that. Miyagi snarks, "Don't know. Never been attacked by tree."
Another case of Miyagi vs inanimate objects from the first film, when some hooligans leave a bunch of beer bottles on Miyagi's truck. They refuse to leave, so Miyagi chops the bottles in half with one swing, terrifying them away. When Daniel asks how he did that, Miyagi replies "Don't know. First time trying."
Pretty much most of Daniel's reactions to Miyagi's eccentricities.
The part where Miyagi, Daniel and Ali trick Pat Johnson into letting her be on the sidelines so she could translate Miyagi's instructions.
Pat: Only Teachers and Students on the competition floor sorry.
Daniel: Oh, but he doesn't speak English and I can't understand his instructions without her. She's his translator.
Miyagi:(speaks Japanese gibberish)
Pat: What did he say?
Ali: He said you remind him of an uncle of his in Tokyo.
Pat: Well I guess it's alright.
Miyagi:(speaks more Japanese gibberish)
Pat: What's that?
Ali: He says you're very kind.
Pat: Oh, thank you.
In the third film when Silver tries to take on Miyagi he starts making Funny Bruce Lee Noises at him. Once Miyagi finishes kicking his ass he waves his hands around in a goofy fashion and mockingly does the same.
Miyagi and Julie discuss her upcoming prom in The Next Karate Kid:
Miyagi: You tell Eric we go to prom. Julie: What do you mean "we", Mr. Miyagi? Miyagi: Miyagi drive car. Julie: Mr. Miyagi, it doesn't really work that way. Miyagi: Then Mr. Miyagi stay at home and wait like anxious parent.
Then Eric shows up to a house full of visiting monks. He takes it in stride, but one can only imagine what he must be thinking. And as if that weren't enough, the poor guy ends up on the business end of Miyagi's Twerp Sweating...while Miyagi is holding a knife. (He's chopping vegetables).
When Daniel asks Miyagi about his skill at karate, he asks what kind of belt he has. Miyagi's reply: "Canvas. You like? JC Penney, $3.98!"
Miyagi: In Okinawa, belt mean no need rope hold up pants!
Likewise later on, during the now memeticWax On, Wax Off scene, Daniel takes note of just how many vehicles are in Miyagi's front yard.
Daniel: Hey, where'd all these cars come from? Miyagi: Detroit!