Lee does his very best to save an ancient giant vase in the middle of a fight with two mooks... then gunfire shatters it moments after he's won.
The first day we see Soo Yung going to school in America (granted, two months after she and her father moved to L.A.), she's quite exuberantly singing Mariah Carey's "Fantasy" in the back of the car. The looks on the faces of her bodyguards in the front seats are just hilarious.
In the second movie, during the spa fight, Carter yanks off the towel of a gangster, and takes a quick glance:
Carter: Man I'm about to whup your old ass because I'm sick of playing games! Yu? Mi? Everybody's asses in here, him!
The scene where the duo confront a Triad member who refuse to speak either Chinese or English. He only speaks French, so they have to get a nun to translate for him, who tries to soften the Cluster F-Bomb the goon is leveling at them. And eventually during the T-Word Euphemism session, Lee (who previously convince Carter not to use any swear words in front of the nun) loses patience when the goon insulted him and hypocritically says "Just call him asshole!" to the nun.
Also the fact that Carter and Lee need the nun to be a translator in the first place to find out who's the goon's boss, but the goon only keeps insulting the duo, and the nun is as if she had no choice but to translate the insult anyway.
For some dark humor, there is when Carter lose his patience and attempt to kill the goon out of anger. But the gun which Lee gave him has no bullet. Carter's response? "I'm trying to kill somebody, man! Damn!"
After a car chase:
Carter: Lee, I'm alive! My whole life flashed in front of me. In three years I'll be married to a Chinese woman. We had three kids, look just like you, only a little darker.
When Carter is in bed with Genevieve:
Genevieve: I have never been with an American man before. Carter: Neither have I!
Carter: Did you know the average Frenchwoman is naked 34 percent of the time?
This, when they spot Genevieve undressing:
Lee: Maybe we should put on a dirty movie. Carter: (shocked) Lee! Lee: Only $9.95.
The outtakes portrays multiple takes of this scene, with Jackie Chan making up all sorts of variants.
Jackie Chan: I like the ones with a story. (take two) I like the ones with a locker room scene. (take three) I like the ones with a shower scene. (take four) I like the ones with a prison scene. (take five) I like the ones with a white girl. (take six) I'm into feet. (take seven) I like the ones with horses. (take eight) I like the ones with hairy women. Chris Tucker: What's wrong with you?!
When Carter overhears the intense fight scene between Lee and Dragon Lady, and assumes they're having wild sex.
Carter: Come on, Crouching Tiger, don't hide that Dragon!
Then, when he opens the door and sees Dragon Lady crawling across the floor to retrieve her knives:
Carter: (to Lee) You are a Super Freak!
"Do you understand the words that are coming out of my mouth?!" and its Call Back: "Do you understand the words that are coming out of my mouth?!" "Nobody understands the words that are coming out of your mouth!"
The bloopers, from all three movies...seriously. You will bust a gut.