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. And yes, the Chocobos can be found on the airship, and serve basically no purpose.
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.
Shinra: Such wanton and vocal destruction.
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!"
Many of the fiend tales are downright hilarious:
The story for Nashorn talks about how he waited in line for hours to touch "it" and when got to "it", he was sucked in by a bright light and found himself in another location. At the end of his tale, his fiend children want him to play with them, but he can't be bothered. Later, the kids find a teleport sphere (save point) and are in awe at how shiny it is. Nashorn quickly realizes that "it" was the same thing that took him away and he dives after it to prevent his kids suffering from the same fate, only to teleport yet again. The kids then wonder where their father had teleported to this time.
The Bolt Drake's tale involves him kidnapping a bunch of kids, only to keep getting pricked by them over and over again until he decides to return them to their parents and vows to go after a calmer kid next time. It turns out that the "kids" were Lulu's dolls, which are known for their Scratch Damage in Final Fantasy X when Lulu used them in battle.
Boris is known for Crying Wolf. At the end of his tale, he cries for help, only for Shinra to ignore him. Turns out Boris really was in trouble since he was attacked by a Behemoth. Shinra comes back and defeats it.
The Tonberry's tale tells how his kind live very short lifespans. The end of the tale reveals why that is; the Tonberries have a nasty habit of stabbing each other, which are a One-Hit Kill. Eventually, all the Tonberries wind up killing each other while the much larger Tonberry tells them to knock it off.
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.
In Chapter 5, after the Youth League members are allowed back into Kilika Temple, Bartello asks the party where Dona is since she wasn't with the group. Yuna and the others can only shrug and assume Dona truly wants nothing to do with him. The Game Over music piece is played as Bartello laments that he'll never see Dona again. When he sees a balloon rise up into the sky, Bartello screams Dona's name and jumps off the staircase, crashing into the jungle below.
Some of the Episode Concluded sequences can be pretty funny, albeit often in a Black Comedy kind of way. Episode Concluded is a "bad" status that the player can qualify for in certain sections if they failed to meet the requirements for Episode Complete. For example, if you talk to Rikku and Paine after Yuna sees the moogle in Luca, they will suggest that she's snapped and suggest returning to the airship. Doing so triggers Episode Concluded. Also, in the Episode Complete version of the Moonflow sequence, the girls are given the option to perform on-stage, but if you've skipped both the "Shave the Hypello" and "Ticket Shelling" missions, then Tobli will end up going on-stage.
Meta example, and mileages may vary, but George Newbern's role as Mevyn Nooj is what landed him the role of Sephiroth, despite him using the voice he gave Superman instead. At least one editor has laughed at this.