The Hypello are pretty comical, such as one of the hot spring scenes in Chapter 4 with Barkeep giving Buddy a massage.
In another moment during Chapter 3, one of the Hypello in Mi'ihen is under attack by a rogue machina. While most victims you rescue run for their lives, the Hypello simply walks away calmly.
The various comical ways Shinra's CommSpheres go down in Chapter 5, from being eaten by a dog to being pecked by a Chocobo to being punched out by Barthello.
In the previous chapter, if you watch the Besaid CommSphere enough times, you get to see the Aurochs practicing blitzball. One of them attempts a sphere shot several times, without success, before kicking the ballinto the CommSphere.
Shinra: "They really suck."
Also within Chapter 4, we find out that Shinra has an invention called the "Chocoporter". Examining the Thunder Plains CommSphere allows you to capture a couple of Chocobos this way...then the Chocoporter shorts out afterwards.
Dona and her former Guardian-turned-boyfriend split up due to their differing philosophies; she supported the Youth League, he supported New Yevon. Check the Kilika sphere enough times and Dona will attach it to a balloon, which she pushes towards him. On seeing it, he breaks the sphere by yelling.
The scene where Beclem kicks a blitzball at Keepa. When hit by the blitzball, Keepa flies backwards into a nearby wall. Also overlaps with awesome.
When Yuna saw a recording of "Tidus"trying so save someone named "Lenne". To say she did not take it well is an understatement. And it was hilarious.
Two, both related to Yuna's heroic tendencies. First there's the part where Yuna just can't say no to helping out, and Shinra's response is: "Hero. Summoner. Doormat." Then there's the part where Tobli is about to get Yuna to agree to sell tickets for him, and Paine figures out before she does that she's about to be roped into something she'll regret.
Paine: Yuna. Run.
The massaging of Leblanc. It's right up there with Mimete's infamous Twister scene from Sailor Moon. Especially if you get the right area. Imagine this line from Yuna, taken out of context
"She fell asleep? I'm that good?"
One of Leblanc's "bad spot lines" is a classic:
"Where are you groping?!"
What's really funny is that immediately after that, Logos and Ormi come into the room and say that one massage and Leblanc is out like a light. "The boss fell asleep again?!" What a come-down for Yuna!
Yuna's reaction to Baralai implying the two of them were supposed to be married.
This Gag Echo when Leblanc stole the half sphere from Zanarkand.
Yuna: Oh, poopie. note Rikku had previously said "poopie" earlier in the game
Rikku: Yunie, don't talk like that.
Yuna: I'm just copying you.
The entirety of the Hot Spring scene. Rikku approaches Yuna, has a peek and says "I know who's got it going on". She then tries to check Paine out as well, only for the two of them to gang up on her. Brother interrupts them asking what's going on. When Yuna responds "a little dip" he says he'll be right there. We then hear a bonk sound and Buddy's voice says "Don't worry, I knocked him out".
Just before the scene, the girls are wondering whether or not to use the spring. Rikku says "on sacred ground". Paine's response? "No one's looking."
The scan description for normal one states "Its fire attacks are a dead giveaway that it's in charge, foo'."
The amusing sound Shinra's suit makes when he's walking around, notably when he's planting CommSpheres around Spira.
In Gippal's Sphere, Auron has a cameo and makes the comment "Even a jackass can save the world."
Wakka shouting Get a Room! when Yuna and Tidus are reunited.
If you recruit him after defeating him, Almighty Shinra has a few quips to him. It still acts as smug as Shinra does, and even hums the "Gullwings Go" theme upon a victory.
Rikku's special attacks in the Festivalist Dressphere. She makes the little goldfish in her baggy grow HUGE and fly at the enemy. One of her battle quotes is even "Fly my pretties!"
Some of the Fiend Tales can be pretty funny as well.
When fighting with the creature creation Brother, he attacks with his butt most of the time.
Buddy's Crosses the Line Twice story about how the Gullwings got their name: Frozen and starving, he and Brother were about to die when a lone gull led them to find the Celsius. Afterwards, they ate the gull.