The quiet moment shared by Edmund and Eustace when Edmund is the first to encounter Eustace after Aslan returns him to his human form - in particular, Eustace's attempt at apologizing for his behavior up to that point, and Edmund's reply:
"That's all right. Between ourselves, you haven't been as bad as I was on my first trip to Narnia. You were only an ass, but I was a traitor."
When the transformation of Eustace becomes known to the crew, Caspian and company are far more concerned with how inconvenient this is for them than with how Eustace must be feeling... except Reepicheep. The mouse spends his evenings keeping the unfortunate dragon company and telling him stories of other people who had suffered enchantments only to later have them removed. "It was meant well, and Eustace never forgot it."
The friendship that grows between Eustace and Reepicheep after the former is transformed into a dragon.
Drinian's minor freak-out when he learns that Reepicheep is the "man overboard". The Dawn Treader's captain, a seasoned, cool-headed, stalwart man, becomes nearly frantic upon discovering that his good friend might be in danger, despite his poor efforts to cover up his anxiety. Reep dousing Drinian with sea water by shaking his fur dry after being rescued is just the icing on the cake.
Fast-forward to Eustace's next adventure in Narnia. What's the first thing Caspian does when he see him? He gleefully asks if Eustace remembers how he broke Caspian's best sword on a sea monster. Decades have gone since that moment yet the king is able to recall it fondly.
A small one from the start of the film, but when Lucy asks if Caspian has finally found himself a queen, he answers "No. Not since your sister," with a soft smile on his face. Three years have passed since the Pevensies left Narnia, but Caspian clearly still thinks of Susan in such high regard. One could only imagine what could've happened if the two of them had been permitted to stay together for the rest of their lives.
In the middle of the movie, Eustace steals an orange that angers Reepicheep enough that he challenges the boy to a duel. Throughout, it's obvious that Reep is actually teaching Eustace how to sword-fight instead of humiliating him, and when Reep pretends to fall overboard, Eustace immediately rushes to the deck, clearly worried out of his mind.
Afterwards, Reep tells Eustace "we'll make a swordsman out of you yet." Eustace starts to smile, pleased with himself ... before remembering that he isn't supposed to be enjoying any of this and walking away with a snide remark. Reep simply chuckles, clearly not believing it.
Captain Drinian allowing Gael to stay aboard despite being a stowaway, and kindly giving her the orange Eustace had initially tried to steal.
The sacrificed slaves reuniting with their loved ones, with Gael and Rince diving over the side of the ship to swim out and meet her mother/his wife.
Halfway through the film, the crew of the Dawn Treader have been stuck in a maelstrom for at least two weeks (if Eustace's narration is accurate) and have a dwindling supply of rations. Instead of turning back, Caspian insists they plow on, not because he wants to earn more glory and find treasure, but because he made a promise to his people (Rince, in particular, who joined the crew for the sole purpose of finding his wife) that he would find and get them their loved ones back.
Lucy's friendship with Gael. Especially when Gael says "When I grow up, I want to be just like you," and Lucy, having worked through her own crisis of self-esteem (from comparing herself unfavorably to her older sister) replies "When you grow up, you should be just like you."
This simple line from Eustace at the end of the film. He and the other two hated each other at the start. Lucy especially says "how will we survive?" when they find out how long they'll have to stay. But going to Narnia helped bond them all together.
Eustace: We spoke often of Narnia in the days that followed. And when the war ended and my cousins went home, I missed them, with all my heart.
One can only imagine Lucy and Edmund telling Eustace all about their adventures during their fifteen-year reign in Narnia, and their cousin eagerly listening to said stories, finally finding something to bond over after being so hostile towards each other in the beginning.
Even before that, where he apologizes for how he was before.
Eustace: Being a dragon wasn't all bad. (sheepish) I mean, I think I was a better dragon than I was a boy, really. I'm so sorry for being such a sop. Edmund:(sharing a grin with Caspian, along with Lucy) It's okay, Eustace. You were a pretty good dragon.
The entire crew being so worried when Lucy gets abducted by the Dufflepuds on Coriakin's island. Props, especially to Caspian and Edmund, who rouse the others at once when they see that she's missing.
Edmund: (drawing his sword with Tranquil Fury) What've you done with my sister, you little pipsqueak?
Edmund and Caspian's relationship in this version does seem more like close siblings rather than two different kings from different times. Before the battle, Caspian even outright tells Edmund that he thinks of Edmund as his brother, and later on, tells all of them that they are the closest he has to family. Even Eustace, who looks so thrilled to be considered in such high regard.
Especially Heartwarming is Caspian helping Edmund with his armor and handing Peter's sword, Rhindon, over to him during the final act.
Caspian: Peter would have wanted you to have it.
The look on Caspian's face when Drinian tells Edmund that Caspian is the one who gives orders on the Dawn Treader. Caspian clearly would not have minded sharing joint command with Lucy and Edmund, and is uncomfortable with repeating Edmund's orders word for word right in front of him.
Edmund wrapping Lucy in a one-armed hug after the battle when she tells him and Caspian that she knew they could do it.
Watching their relationship unfold throughout the whole film is quite heartwarming. They've come so far indeed from the two siblings who could barely stand to be around each other in the first film.
He even rubs her arm comfortingly when Lucy, clearly close to tears, presses into him after seeing Gael reunite with her mother.
When Lucy and Caspian bid each other goodbye on the shores of Aslan's Country, the two forego all formalities and hug each other tightly. Caspian even lifts her up a bit when he does so.
Eustace, after undergoing some much-needed Character Development, shedding tender tears when Reep decides to stay in Aslan's country.
Eustace: (crying heavily) I won't be able to see you again.
Reepicheep: What a magnificent puzzle you are, and a fine friend. It has been an honor to fight by your side.
A meta-one, but apparently while filming the scene where Lucy, Edmund, and Eustace board the Dawn Treader for the first time, Georgie Henley (who plays Lucy) slipped off the elevating platform she and Ben Barnes (Prince Caspian) were standing on. Luckily enough, he managed to catch her, much to the relief of her mother, who was also on-set at the time.
Ben Barnes: She slipped on that (the platform) and fell, and I managed to catch her and pull her back up on the thing. Her mum was like "THANK YOU!" and I was like, 'Don't worry, that's what I'm here for.'