While not necessarily a bad thing, the whole series had almost no humor. What little could be found was probably accidental and subjective, or intended to be extremely subtle. However, in Endless Waltz, there's one humorous moment when Heero asked Duo to punch him.
In episode 12 Trowa had to let Heero know what happened after he tried to blow himself up. Trowa contemplated whether or not he should off himself with honor as well. Heero's advice on the manner made the normally stoic Trowa laugh.
Trowa: What would happen if Oz used the colonies as a shield again. Or should I be following your example.
Heero: In that case I got one warning. It hurts like hell.
"Heeeeeerooooooo! I am right over here so come and KILL ME!!"
In the second episode, he comes across Heero about to shoot Relena, and steps in to save her, wounding Heero with his own gun. Relena chastises him and begins bandaging Heero, prompting Duo to wonder: "Great, how come I ended up as the bad guy here?"
After rescuing Heero from the hospital, he's complimenting Heero's Wing Gundam when he turns around to see Heero snapping his broken leg into place. Duo is thoroughly Squicked by this: "I can't take much more of this. He just goes and puts a broken bone back into place. Man, that just totally grosses me out thinking about it."
"Oh, man, Quatre loves to blame himself for everything if you let him. I wouldn't be surprised if one day he starts saying his lack of effort is the reason there's no air in outer space."
Duo wondering about why he tries to help Heero: "He's antisocial, thinks he's Evel Knievel, and hardly speaks!" (He groans and throws his hands up in the air.) "You've got such a gloomy personality, why don't you give up and stop pretending to be human?"
Duo watches in awe as Heero takes off in the previously damaged Wing Gundam, understandably shocked that he had managed to complete the repairs to his Gundam with practically no supplies... then he finds out that Heero succeeded in doing so by ripping parts from the Deathscythe. Needless to say, he wasn't happy. Even funnier when you realize that Duo actually offered earlier to use Deathscythe's parts, but he likely meant spare parts rather than the ones inside the suit.
(referring to attacking an enemy base) "See ya! We don't want to be the last ones at the party now, do we? PS: don't blame us if they run out of treats."
And then later:
Sally: "Why thank you, Duo. You were kind enough to leave me plenty of good treats."
Duo: "If you're joking, that's cruel, but if you're being sarcastic, that's even worse!"
Let's not forget the time when he found the Five Mad Scientists in the White Fang battleship. He totally looks like "... uh. what the FUCK are these people doing here". And then bails the HELL out.
The creators of the manga adaptation, instead of creating a brand-new backup feature, instead continued the Yonkoma from their G Gundam adaptation, now renamed Go For It, Domon W!, and featuring characters from both series doing all sorts of crazy, non-canonical things. Like its predecessor, it entirely runs on Rule of Funny.
The Ground Zero manga give us something that you realize is this only through Fridge Logic: Treize met his wife (and Mariemeia's mother) because Heero put him in hospital and she was his nurse.
Giant Flying Golden Jellyfish hallucination brought on by the ZERO system.
Those were actually images of Deathscythe with a golden aura, but yeah, it did look pretty silly regardless.
When Heero gets his Gundam back, he notes how the self-detonation button is no longer wired properly. The mechanic notes that it was a direct order from Zechs. Trowa dryly notes that Zechs probably wants to finish the duel this time around.
Heero has to use an alias to enter that school. What name did he choose? Duo Maxwell.
Relena comes across Heero, who is reading on a bench outside her mansion in the Sanc Kingdom.
Relena: May I sit with you?
Heero: It's your country. Do what you want.
In episode 46, Quatre suggests that the reason Heero left for the Libra without Wing Zero is to "rescue" Relena. Wufei responds that he no longer considers Heero to be the "most sane among us." It's a mix of his deadpan delivery and Heroic Self-Deprecation that sells it.