The Love Triangle between Alanna, Jon, and George becomes increasingly complex... but there are no petty rivalries, no distracting arguments during crises, people communicate clearly, every participant is a mature adult who respects and sometimes is friends with every other participant. There are moments of petty immaturity, but they are far from the norm and don't go without someone calling them out.
Myles legally adopting Alanna in the third book through a Bazhir ceremony, as a capstone for their relationship in general. From the start, "Alan's" friends were angry at Baron Trebond for so neglecting his children, and Myles took it upon himself to recognize Alanna as a bright, likable, and worthy child, giving her the guidance and affection she deserved. After Alanna loses the man who was never really a father, Myles steps up and becomes her father in name as well as sentiment.
During the climax of Page, Lalasa starts talking about how she kept waiting for Kel to turn out as a Bitch in Sheep's Clothing and almost being frustrating when Kel continued to be genuine, to trusting her and gaining confidence in herself (and her ability to take care of herself) because Kel believed and taught her that she should have it, and having faith that Kel would come to rescue her. In the face of this, Kel is able to break out of her panic and continue the long climb down Balor's Needle.
After the above, Lord Wyldon finally expresses his approval and respect for Keladry. He does so by saying he wishes she had been born a boy, but it's a huge moment for a man who, at the start of the first book, told the Lioness with great sincerity that girls were not meant for knighthood.
A minor moment during Page is when, after finding out Lalasa's been kidnapped, Neal offers to go with Kel, knowing full well that they might be forced to repeat all four years of page training. Kel refuses to let him on the grounds that he hated it, but he still tries to insist on helping until she finally manages to get him to leave. And Kel, assuming she'll be forced to redo training, even offers to let him be her knight-master when she becomes a squire.
Squire: Peachblossom taking great offense to Greystreak the centaur's attempt to buy Kel. Especially if you've ever had an intelligent, argumentative, prickly horse decide to adopt you as his or her particular person.
After all their years of clashing, Keladry tells Wyldon that he's the kind of knight she wants to be. He tells her simply:
"I am not," he said. "But that you believe it is the greatest compliment I will ever receive."
A book later, when she returns from Scanra having disobeyed a direct order and gone to rescue her people, she tells him to go ahead and yell at her; she deserves worse. His response? A gentle kiss to her forehead and these words:
"You are a true knight, Keladry of Mindelan. I am honored to know you."
An offhand remark by Cleon in Squire makes Kel realize that her friends have gotten into a lot of fights over the years over insults to her, without her knowledge. She feels humbled, but Cleon says that she's worth it.
Yuki gives Neal her shukusen as a gift after he survives his Ordeal. He carries it in his belt during his knighting.
Kel finally meets Alanna at the end of Squire and learns that Alanna was her Anonymous Benefactor, after eight years of being banned from seeing the hero who inspired Kel to try for her shield in the first place because of political nonsense. Alanna assures Keladry that she did care about the first openly female page, knowing from Neal that Kel worried about it, and goes on to tell her that she is just as important (if not moreso) to the girls of Tortall as Alanna because nobody can say that Kel got by with magic or divine favor, and how proud she is of Kel even though they never got to meet properly. Kel's awestruck reaction to Alanna showing up at her room and being praised by someone who's both a hero to the realm and a personal hero makes it seem worth those eight years.
In Lady Knight, when everyone (and we do mean just about everyone) showing up to help Kel rescue the refugee children from Blayce, even on penalty of a traitor's execution.
Also heartwarming is the absolute trust of Kel the kids have; during the rescue, a simple signal is enough to keep them totally silent and one of the youngest kids dashes to hug Kel as soon as he's safe.
The beginning of Squire, when Raoul tracks Kel down in the tiltyards and asks her to be his squire — not because he feels sorry for her, but because he thinks she has tremendous potential not just as a knight, but as a commander, and wants to nourish that talent. Then admits that he'd meant to ask her straight after the 'big exams', but the Own was called away and he'd only just got back. All that time Kel spent worrying, and the best knight-master she could ask for was waiting in the wings.
Beka is unable to honor the dead properly due to the urgency of her quest, even though she can't bear leaving them for scavengers. So the Black God shows up and does it for her, calling her his most faithful priestess. In a world where Jerkass Gods are the norm, there's something sweet about a genuinely nice god who cares about humans.
Also from the same book, after Beka has spend a long time moping about her dead fiancé, who she secretly no longer loved and also blames herself for the death of, Farmer proposes to her.
The end of Mastiff, when the King and Queen, after signing a proclamation to abolish slavery, have Beka—the common Dog—put her signature under their names because they never would have realized its evil without their son, whom Beka rescued, and he told them that was what Beka would most want in repayment. And the whole gathering, led by Holborn's old partner, chants her new appellation of Mastiff.