In Little House in the Big Woods, little Laura's rather upset because Mary has blonde hair whereas hers is, in her own words, "ugly and brown". Pa then points out that he has brown hair, too, which makes her much happier with her own.
In These Happy Golden Years, Almanzo making it clear that he will continue to take Laura home every Friday and then back to her school on Sunday even if he has nothing to gain from it himself. To elaborate: the previous weekend, Laura told him up-front that she was only going with him in order to get home, so he shouldn't feel any obligation to come. On Friday afternoon, the temperature is forty below and dropping and Laura is absolutely certain there's no chance at all he's going to come. He does.
On the same note, once Laura's teaching job is over and she's back at home, she discovers that her school friends are all going sleighing and clearly having a wonderful time. Realizing that her extended absence has caused her to be left out, she feels quite depressed - until Almanzo shows up at her door asking if she'd like to go sleighing.
A subtle one in By the Shores of Silver Lake. At the beginning of the book the Ingallses move west to Dakota Territory, even though Ma doesn't want to, because Pa (as ever) wants a homestead and has a job offer at the railroad camp in the meantime. Once they're there, Laura wants to go further west, and is jealous of her "wild" cousin Lena whose family is going to move on. Pa obviously feels the same way but tells her he promised her mother they would settle down somewhere where the girls could go to school. One night Laura takes Carrie out to slide on the frozen lake, and by following the reflection made on the ice by the moon, they end up going all the way across. They see a wolf and run back to the house, where Pa is surprised to hear that they got that far away in the first place.
"We followed the moonpath," Laura told him. Pa looked at her strangely. "You would!" he said.
In These Happy Golden Years, Laura telling Almanzo he may kiss her goodnight, after she accepts the engagement ring. It's sweet and a little awkward, and it's Laura clearly trying, when she's been mostly reserved towards him all along.
A lot of her earliest interactions with Almanzo are both sweet and somewhat funny, mostly because while the reader can easily see what he's doing, Laura is fifteen and completely clueless. He's being as romantic as was actually possible in a frontier town, and Laura does not see it. It takes Mary Power pointing it out to make Laura realize hey, surprise, she's being courted. (The narrative explicitly mentions that Laura has no idea why a 'grown-up' would want to spend time with a girl still in school.) Somehow, this comes off as endearing, rather than creepy.
Rose's birth. The First Four Years spends a lot of time fussing and figuring out the Wilders' financial situation, and this is the only time it's not made out to be a dire annoyance.
There were doctor bills, but, after all, a Rose in December is much rarer than a rose in June, and must be paid for accordingly.
The Caroline Years:
In Across The Rolling River Caroline's relationship with Miss May and how that inspires her to become a teacher.
And her growing friendship with Charles Ingalls, especially their Friendly Rivalry over the spelling bee.
In "Little City By The Lake" Caroline's friend Millie standing up for her when the other girls look down on her mother making her dresses.
Caroline's aunt doing her best to give Caroline a new dress for a ball despite Caroline's protests.
The Charlotte Yeas
On Tide Mill Lane: The town celebrating when it's announced the war is ending and later the Tucker's delight when Will (Lew's striker in the forge) returns home.
Throughout the book Lew shoulders a much larger workload in the forge because he doesn't want to replace Will. When Will returns, he's lost a leg and isn't sure if Lew will give him his job back. Lew and Martha both tell him he's ridiculous for even suggesting that they wouldn't want him.
Overall just how happy Martha is after her struggles growing up in the previous series. The narrative makes it clear that she loves every minute of her life in America from looking after the children, cooking without help, being married to 'the finest blacksmith either side of the Atlantic' visiting their neighbors and her freedom in living as a commoner.
And by extension, how happy she and Lew are together. It's pretty obvious Martha kept her rebellious streak from her childhood, but rather than being ashamed of her, Lew clearly adores how spirited she is and doesn't mind saying so, whether its commenting she could frighten the president if she wanted or laughing at her cheering for him in public. It really gives you a look at why they both risked so much to marry each other.
A particularly sweet scene occurs when Lew insists that Martha buy a dress for herself. Martha objects saying they need other things and fine clothes are wasted on her 'common chicken feathers'. We get a brief look into Lew's feelings for Martha.
Lew: My Martha, a common chicken? I think not. Ye're a skylark, of course. Soars high, nests on the ground, sings the happiest song in the heavens. I ought to have seen that right away.
The Martha Years:
"Little House In The Highlands": Martha making up with her brother Duncan after he loses her doll.
"Down To The Bonny Glen": Martha's new governess Miss Crow subtly comforting her about a ruined sash and Martha's growing affection for her after loathing her previous governess.
Martha breaking tension between her brother Duncan, and their friends Lew and Ian over the suddenly realized class differences, by challenging Lew to a footrace. He clearly realizes what she's doing and plays along.
"Beyond The Heather Hills": Martha bonding with her older sister Grisie after three books of sisterly rivalry.
From the same book Lew helping Martha get craft supplies when she's stuck in bed, including giving her his own knife. Even the gruff, no-nonsense Cook is touched and calls them quite a pair. Bonus points for Martha never doubting he'd do everything he could to help her. And in the end Lew insists she keep the knife so Martha gives him one of her home-made dolls for his little sister.