The whole game arguably - what might be the true major theme is the friendship, the bond, between every member of the cast as they become True Companions.
The "Karol's Growing Up" skit, triggered when Karol uses a Mystic Arte in battle for the first time.
A lot of Yuri's interations with Karol are like this, as we see Yuri grow from being annoyed by him to becoming something of a Big Brother Mentor to him.
Actually, from the start, though he's annoyed by Karol, Yuri treats Karol well. Considering his reputation in Danghrest, Yuri is probably one of the first people to be genuinely nice to him. The other is probably Nan.
Yuri's fury at Estelle saying it's okay to die after she finds out the Awful Truth about the Children of the Full Moon is this when you consider his character. He really does care, even if he's not too good at expressing himself.
When Karol is fighting the Baitojoh by himself in the Blade Drifts of Zopheir, and Yuri and Judith are yelling at him to run, we get this from Raven:
Raven: Move, damn it! If ya don't, the kid's gonna...
When Yuri tries to go off to Zaphias by himself to "do what has to be done", he takes a brief nap in the forest after having a lonely chat with Repede...only to be kicked, punched, and fireballed awake by the rest of the party (who were in fact led there personally by Repede) for trying to bear the pain by himself.
Once they get to Zaphias, there are two skits that activate that have Raven console Yuri and Rita. It's nice to have the old man show his experience as much as him supporting those two who might be taking the whole situation what with Estelle possibly being too far gone to be saved the worst of the group.
"I WANT TO BE MYSELF...I WANT TO KEEP ON...LIVING!"
After Zaphias, the whole party bands together, to save Estelle from Alexei and prevent her power from going out of control, lending their strength to power Rita's formula to free her from the sphere she was imprisoned in.
And after she's free, Estelle falls into Yuri's arms.
Yuri: Welcome back.
Estelle: It's good to be back.
The night before the party heads to Zaude, Yuri has a conversation with Flynn in the latter's room about the challenges the world now faces. They've butted heads ideologically over the course of the game, sometimes violently, and their friendship has been repeatedly tested. But, when the camera zooms in on Flynn, you can clearly see that he...has framed and mounted a crayon drawing of him and Yuri as children, right at eye-level at his desk.
The same night, you find out from Raven that Estelle smacked him on the head and said they were even. Think about that for a second. Estelle was imprisoned, mind raped, tortured into doing Alexei's bidding, and forced to use her power (the same power that she had used to heal every injured person she could find) to hurt people, including her friends. All because Raven kidnapped her in the first place. And all it takes for them to be even is a smack on the head.
You also can find Karol with the Lower Quarter people. What's he doing? Just putting his various skills to use to fix up their important things that got crushed or battered due to the crisis. Repede even helped out there. Yuri couldn't be more proud and Hanks makes it very clear that he's also impressed by them. Consider Karol's past in Dahngrest (with All of the Other Reindeer applied to him thanks to his guild hopping) and this is extra heartwarming as it proves just how far he's come.
When facing Alexei at Zaude, one by one each character challenges his justifications for his crimes. Considering his pastactions, Raven's is particularly poignant.
Raven: The ends don't always justify the means, boss. These kids taught me that.
After Zaude, when Yuri wakes up in his room after falling off the tower — one by one you find your party members, who have been searching across the world for him for days. All of them express open, emotional joy that he's alright (special mention to Estelle pretty much glomping the guy), and there are not one, but two full skits where the party discusses how happy they are that they're all finally together again.
Belius's revival as Undine counts, especially considering the tragic circumstances of her initial death.
The night before the final battle, everyone in the party gets a Friendship Moment with someone else. The conversation topics range in tone from musing on one's place in the new world, to...Raven telling Karol that his life's dream involves being surrounded by hot women, but all serve to cement the group's True Companionship and inseparable friendship.
The PS3 version includes Patty talking to Flynn. She shows her real age by dispensing advice to him about not taking all burdens on himself. Flynn's reaction to this, that of thoughtfulness followed by appreciation, is poignant and just as heartwarming as the other interactions.
Special mention to Yuri and Estelle's conversation, which has the music box render of Ring a Bell playing under it, and contains what can be interpreted as a sweet love confession:
Yuri: "The Adephagos won't kill us. We'll live on." Estelle: "And I'll be able to stay with everyone. With you." (There is a long pause where they look at each other, broken when Estelle looks at the ground/her hands) Yuri: "Thanks. I feel the same way."
Yuri and Flynn's fight to settle the differences between the two of them. The two of them are just snarking at each other and show that they're best friends who always have each other's back.
Even better, a line that Yuri might have been waiting to hear all game, even though he's not there when it's finally said aloud:
Rita makes it clear that she really doesn't like Repede over the course of the game, to the point she almost never uses his name. She calls him "dog" in the skits and one of her battle quotes being a sarcastic "Good job, Spot" (which started life as a scathing "Pretty good... for a dog"). However, battle with them together at the end of the game and Rita will sometimes say in a genuine, warm tone: "Nice job, Repede!".
Some of the interactions between them make them come off like Vitriolic Best Buds and it's darn cute if you think of it like that- two of the skits can be seen as a pair: "Joy and Sorry on the High Seas" (Skit number 371) and "Not so Good With Heights" (number 373). In the first, Rita decides to make fun of Repede's fear of water by dragging him to the edge of the Fiertia. In the second, Repede does the exact same thing to the acrophobic Rita when they're in the air. In Repede's 100 Man Melee skit ("A Dog's Thoughts on Battle"), they start a fight with each other (it should be noted Rita is the only person Repede ever fights with- he "plays" with Karol and messes with Raven, but Rita's the only one where it's a fight) When you think about it as Repede getting revenge, Repede's capable of being just as much of a kid as Rita and Karol. On the nicer side, there's a skit where Rita is allowed to name Repede's Mystic Arte over Karol and Raven's suggestions ("The Christening"), a skit where Rita is clearly jealous that Yuri can understand Repede ("Dog Language"), a skit where it's clear Repede actually does like Rita ("Rita and Repede"), a skit where Rita asks Repede to help her with Raven being a pervert even though Yuri is also right there ("Manly Musk"), and two where Rita and Repede share in mutual exasperation over Raven ("A Change of Pace" and "From Mind to Game"). It's kind of adorable.
How about Leblanc, Boccos, and Adecor realising that the people of the Lower Quarter were left behind (this meaning they actually are familiar with the faces of people in the Lower Quarter), doubling back, and taking them to the castle when they couldn't get them out of Zaphias? They fight very hard to protect the people of the Lower Quarter from Alexei's supporters, people the other knights didn't even seem to notice had not been rescued and people nobody else even bothered to try to save because of how thick the mess was down there. They went against orders to do it, too, essentially defying everything the Lower Quarter (and Yuri especially) has come to expect of knights- especially those three, since they have a reputation for "bullying Yuri". If you ever had any doubts about them, they should have been cleared with that. Raven even compliments their valour, which means a lot to them, considering he's their commander whom they deeply respect. What they did is both this and their Crowning Moment of Awesome.
When you go to Port Nor after Heracles, Pauly, the little boy who you rescue from Ragou's place, will tell Yuri he drew him a picture and he wants to show it to him sometime (if you talk to Pauly). The picture? It's apparently of Yuri himself.
How Karol gets his Bug Breath arte. Raven decides to play a joke on him and say a swarm of bugs is coming. Rita, who up until now has been very rude to Karol, promptly sprays Raven in the face with bug spray and reassures Karol. She walks over to him and gives him the bugspray- "Here, take this. Aspio-brand insect spray, the best to keep the bugs away!". Karol is very surprised by this, but Rita doesn't fire up like usual, simply saying she really doesn't mind and tells him not to spray it near people. Even her teasing about his freaking out in one of the skits is pretty lighthearted compared to how she usually is.
If you complete the Monster Book, you get this skit (PS3 version).
Very easy to miss and crosses into Tear Jerker territory, but try bringing Karol to the fight with Schwann. He says this, before the boss in question interrupts:
"I really liked you, Raven. I couldn't tell you before, but I... If my dad-!"
Oh, and the entire party exchange after that fight, where even Rita wants Schwann to leave when them, even though he's the one who handed Estelle off to Alexei, and she looks as depressed as Karol. Schwann, or rather Raven, then pulls a Heroic Sacrifice to get the party out alive. Rita and Karol, again, have the most upset reactions to this, and from the tone of her voice, she's holding back tears. It's also Rita who tells Leblanc and the Tweedles that their captain is the only reason the party is still alive. From Rita, considering her animosity towards Raven, that's as heartwarming as it is heartbreaking.
Rita is usually conspicuously absent or at least silent when you talk to kids, and indeed most of the talking with children thing is handled by Yuri, Estelle, and occasionally Repede. However, talk to the Krityan child in Myorzo, the one who has you race Ba'ul, and Rita does most of the talking. She is the one who sticks up for Ba'ul (though it's Yuri that corrects the kid on "Ball's" name). When you talk to him to get Judy's Into the Sky costume, check the speech bubbles- it's Rita who tells the kid he's cool for being able to count 1,000 FS.
Considering this sidequest pops up in the third arc, it also works to show how Rita's friendship with the rest has affected her; she's much more open to talking to people and much less belligerent.