After beating Bonus Boss Dark Ifrit in the PAL version, you're treated to a cutscene in which the SOB who summoned it is eaten by a fiend. Although the Dark Valefor one is pretty funny too (Evil Bald Summoner Guy gets pwned by a little girl, and runs away from the angry villagers).
The party meets Dona. She tosses off insults at Yuna, while her massive guardian stands behind her. And then...he speaks. "You're Auron, aren't you? May I shake your hand?" Dona is left completely wrong-footed.
You forgot to mention that the insults were about Yuna's many guardians, referring to them as "riff-raff". And Auron is a legendary guardian. Wakka and Lulu then mock her for inadvertently insulting such a famous figure.
"Touch me with that hand and I'll remove it!"
Then of course there's all these exchanges in battles:
Tidus:(to Auron) "Don't break any bones, old man!"
Wakka:(facing a Behemoth) "How many steaks you think we can get outta this?"
Rikku:(facing a Dark Flan) "Wow! Say, is that edible?"
Lulu:(using Bio for the first time) "This might help your complexion."
Wakka:(facing a Giant Worm) "Where's de early bird when you need 'im?"
(When Yuna, Lulu, and Wakka are all out at once...)
This troper believes the infamous laughing scene is this in a So Bad, It's Good kind of way.
Tidus clowning around on the S.S. Liki with the binoculars always makes this troper start giggling. Specifically when Tidus first grabs them and all the player sees are the belts on Lulu's skirt. Pan upwards to her chest and Lulu scowls. A moment that's both funny and absolutely adorable is Yuna running to make sure she's still being seen in the binoculars.
Try talking to the binoculars guy after that. He runs from Tidus in fear!
When the party is reuniting in the Bikanel desert:
Rikku: "Umm... There's something I wanna tell you guys, but promise not to say anything!"
Wakka:(camera zooms in on his face) "HM?!" (glares)
Rikku: "No glaring, either!"
Another part that happens in the desert is when the player finds Kimahri, who keeps trying to walk up a steep sand dune despite falling back down it repeatedly.
Auron's story about Jecht meeting his first shoopuf. He was drunk and thought it was a fiend, so he attacked it. Braska and Auron had to offer all the money they had as an apology, and Jecht never drank again.
Also a CMOH for Tidus, who always wished his father would stop drinking.
After Tidus' commentary at Home about the fate of summoners, we get this sole line from Kimahri: "It's quiet. Kimahri goes now." This troper finds it unintentionally hilarious.
Rikku's freak out in the Thunder Plains, followed by the party coming across an inn and Rikku begging to stay there. The way everyone except Tidus keeps walking away from her as you talk to her is too funny.
Made even funnier by how the scene ends with the rest of the party finally giving up and staying at the inn.
Auron: "Fine, we rest. She's worse than the storm."
Kimahri telling Tidus in no uncertain terms to hold still until Yuna gets her new aeon at Djose Temple.
Kimahri: "Pick spot. Shut up. Wait."
"RIDE ZE SHOOPUFF??"
An unintentional moment is made by an animation error on Seymour during the wedding scene, while Mika is threatening Yuna (at around 4:28).
The whole cast good-naturedly poking fun at Yuna when she wakes up with bedhead. The entire scene is hilarious, but Auron really takes the cake:
This line is so good, in fact, that there's a Call Back to it in X-2, as one of the two lines spoken by Auron in Shinra's character database.
Tidus and Rikku talk on Mt Gagazet about what to do next. Rikku jokingly tells Tidus he sounded like a leader. Tidus replies "Star player of the Zanarkand Abes, didn't you know?" to which Rikku gives a magnificent mock bow.
Early in the game if you have Tidus and Lulu in the party Tidus will celebrate winning a battle excitedly and Lulu will snark "you're a modest one".
If you talk to Wakka after seeing the quick bit of Yuna about to marry Seymour.
Wakka: "I'm glad Yuna's okay and all but what's with those fancy clothes."
Depending on who Tidus' "partner" becomes during the game, there's a scene where Tidus discusses the idea of Yuna getting married with him/her. If it's Lulu then you have the option to say "You're more my type Lulu". Her response?
Lulu: "Hmm, interesting. I suppose I could add you to my list. But you'll have to be patient, little boy".
After you rescue Yuna from the Al Bhed in Luca, Lulu tells the story of Yuna's parentage, then asks Tidus not to tell Wakka because of his Fantastic Racism. Tidus then realizes they need to let Wakka, still playing a delaying action against the Al Bhed Psyches, know that they've rescued Yuna, but Lulu is a bit slow on the uptake.