It doesn't top his earlier quip in Part II. After they arrive in Okinawa and see a poster of Sato chopping a board with his bare hands, 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 giberish-
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 Japenese gibberish—
Pat: What's that?
Ali: He says you're very kind.
Pat: Oh, thank you.
Pat: -looks bewildered-
In the third film when Silver tries to take on Miyagi he start 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 actually 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)).
Dre's mom tells him to practice his Chinese, so he turns to a Chinese guy and speaks (very poor) Chinese. The Chinese guy's response was absolute gold.
Dre: *Attempts to say "What's your name?" in Chinese, and not doing a very good job.* Chinese Guy: ... Dude, I'm from Detroit.
It should be noted that this is the part where the title card comes in, signifying that this will be a long and difficult movie for Dre.
The last time Dre's mom tells him to pick up his jacket, she says it quietly but with such force.
PICK up your jacket!
When Mr. Han tells Dre's mom that Dre is his only student, she has this sort of "Oooookay..." look.
During the Tournament at the end, Dre scores a point against one of his early opponents with a fast shoving motion. The slow-mo done for the crowd draws attention by pausing on the face Dre is making at that precise moment.