After Yumi's defeat in the prefectural finals, she tells Momo that she feels like going off and disappearing somewhere. Momo then says that if she does, this time, Momo will be the one to call her name and find her.
At the end of Mihoko and Hisa's individual match, when Mihoko has all but given up on Hisa remembering her, Hisa tells her after the match ends that she played against her once before, and "Your eyes are so pretty, I wonder why I had forgotten," causing Mihoko to tear up in response.
Koromo coming to the realization after the prefecturals that her teammates have been her friends the entire time.
Nodoka's flashback sequence at the start of Zenkoku-hen Episode 3, and one bonus chapter in the manga begins on a somewhat depressing note, with her having drifted apart from Shizuno and her other friends after entering middle school (before her transfer to Takatoobara), and essentially coming to the conclusion that if she had known things would turn out like this, she never should have made friends in the first place. But in the course of a relatively short period of time, she meets Yuuki, joins her school's mahjong and realizes that even if friendships don't last forever, it's important to treasure them.
From the otherwise largely comedic "Saki Biyori", there's a somewhat surprising example in Chapter 24, which focuses on Hisa and Mako during the last year (Hisa's second year of high school and Mako's first), when they were the only two actual members. After pondering some bizarre and less than successful ideas to increase membership, they ultimately conclude that if people like mahjong, they will come naturally, and shouldn't feel forced. The ending text, which otherwise often makes a joke at the expense of one or more of the characters involved, concludes with "Your worries will be over soon, Takei-san and Someya-san, next year no less than four new people will join."