Grace adopting an abused puppy that was being groomed for dog-fighting, at the end of one side-quest in Case 6.
At the end of One-tooth Sam's side-quest in Case 11, he vows to make Cooperville a better place to live in honor of his late wife's memoryafter getting back his lost wealth.
When Jones is out of commission halfway through Case 31, Ramirez steps in to be your partner. He's genuinely worried about Jones despite how hard the latter is on him. It just goes to show how much of a nice guy Ramirez is throughout everyone criticizing him constantly which is likely what helped make him so popular with the fans.
Ramirez: Oh, <Rank> <Name>, you've seen Inspector Jones? How did he look? Do you think he's going to make it?? I'm so worried about him... You know, Jones was the one who helped when I started my work as a policeman. He was like a mentor to me! Oh, I know he likes teasing me, but he's got a good heart. And, well, I still have many things to learn, after all!
At the end of one side-quest in Case 41, Cathy King (Chief King's granddaughter) confesses that all she wanted was to dance with a nice guy at her prom ball, which got ruined by the actions of the Rorschach Reaper. She then asks Alex if he'll dance with her. Jones helps.
Alex:(blushing) A-a dance? With me? But—but there's no music! And no ligh—
Jones: Of course this idiot would love to dance with you, Cathy! Go on, have fun! (to the player) Come on, (player's name). They need some space, and I've seen the piles of burgers on the buffet table! It'd be a pity to let them go to waste!
At the end of Case 28 of Pacific Bay, Amy started to question her purposes of being a police officer after her high school sweetheart, Bobby Prince, was arrested for the case's murder. And the one who managed to snap her out of her disillusionment was none other than the grumpy, irritable and cynical Frank Knight.
Case 32 starts out with Frank Knight buttering up the Player Character. As it turns out, his daughter's favorite book is being turned into a live-action movie, and she is a huge fan of the actress. Frank wants to get his daughter an autograph so that she'll speak to him again.
Case 44 of Pacific Bay (Case 100 overall) is a big one for Frank Knight. Chief Marquez is one of the suspects in the murder of Colonel Spangler and he becomes emotionally invested in the case. Much of the case has him wishing that Andrea is innocent and he even threatens to leave the police force if she's guilty. Keep in mind that Andrea singles out Frank for discipline more than anyone else so it shows just how much he really cares about her. He also asks the player to give him some privacy so he can have a private conversation with her after the real killer, Pearl Montana, is sentenced.
Amy and Russell's Big Damn Kiss at the end of Pacific Bay's Case 56.
How the team forgave Frank Knight for his crimes and attended his funeral.
In Case 9, a runaway named Benjamin Scott reveals that he left for Africa because he's embarrassed by his family back home. Upon hearing this, Elliot goes out of his way to look for the kid and tell him that his family loves him, and that he should be happy because Elliot himself wasn't so lucky when he was younger. This hints at Elliot's Hidden Heart of Gold, implying that his Jerkass personality is just a facade. When Benjamin reaches a reality crisis in Case 12, Elliot is the one to console him and convince him to go back to his parents.
When Ambassador Stern's son is traumatized by the events of Case #12, Lars befriends him and manages to help him feel better.
The end of the Eurasia arc has this adorable moment: Angela shows off her nesting doll of Jack, and Jack wonders why his doll is the smallest. Angela says it's cause he's the "baby" of the team (being the youngest field agent), and while Jack is confused, he thanks her for making him feel loved.