Lennie Briscoe was, after fourteen seasons, the first person on Law & Order to retire. One cop got shot, another was benched with minor paralysis. One ADA died in a car crash, one returned to private practice, the original made a move to private practice, one moved on to grander federal work. Lenny realized he was getting old and decided to hang up the badge. As he packs up his desk, all the actors get double points because Jerry Orbach was, at the time, the series Long Runner. He was moving to a part time gig at Law & Order: Trial by Jury, but...
Briscoe: Well, it's nice to go out on a win.
Van Buren: This place just won't be the same without you, Lennie.
Green: Hey, man, that DA thing works out, good luck. They gettin' the best in the city.
Briscoe: No, I'm lookin' at them.
McCoy's relationship with Claire Kincaid was mostly a source of humor or of angst for her. But after her death, it was serious business for Jack. Only lightly hinted at by Jamie Ross, but one time he very nearly went over the Moral Event Horizon to convict a man of murder when the law said he deserved a much lighter sentence for driving drunk... Claire was killed by a drunk driver. The moment when the man begs for mercy, saying, "Please, I'm not a monster." and Jack responds by presenting the evidence proving he's not... The entire episode is proof that Jack didn't take his affair lightly, and that moment proves that Jack, too, is not a monster.
Ben Stone's departure is one. After a miscalculation on his part has tragic consequences, he resigns. After a few words with Schiff about his immediate plans, he just gives his former boss a warm smile and a friendly pat on the shoulder, then leaves. It's a quiet moment that shows the almost father & son relationship between the characters, one that McCoy and Schiff didn't really have.
17x19, "Fallout" deals with a Russian KGB agent who comes to the US to track down the men who kidnapped, trafficked, and murdered his daughter. Turns out they'd kidnapped both of his daughters and offered him a Sadistic Choice: which one would he like back? He confesses to this in a Tear Jerker scene that pushes Jack to his limit: Man 1, 10 years. Connie wonders how the daughter couldn't understand her father's choice. Jack replies that some daughters aren't that forgiving. The episode ends with Jack at a restaurant when a young woman walks up.
Jack: I wasn't sure you were going to come.
Woman: How you doin', dad?
Jack: [grins like an idiot]
"Phobia" A gay man is beaten to death and his adopted son is kidnapped. His grieving partner can do nothing but wait as the detectives frantically search for the missing baby. When they finally find him and hand him over to his father, the man quietly tells them, "Thank you for my son". The detectives smile and walk away, clearly happy to have gotten at least one win in the midst of all the chaos.
"Challenged" (season 19, episode 2): Detectives Lupo and Bernard are interviewing some developmentally disabled men who live in a group home about something they may have seen on a visit to a nearby park. The men are excited to talk to real live police officers. One of them is especially fixated on coffee at the stationhouse: "Do they have coffee at the police station? Can you drink as much coffee as you want?" When Lupo and Bernard return to the home for follow-up questions, they bring some police insignia patches... and a Thermos of police station coffee.
Boy Gone Astray (Season 20, episode 7): Lieutenant Van Buren is receiving chemotherapy and is feeling ill because of it. Her son provides her with marijuana. Someone at the precinct notices the smell. Cue arrival of head of the precinct. Instead of reading the riot attack, he proceeds to tell Van Buren how to 1) get it with a medical licence and 2) how to hide the fact that she's been smoking weed because he knows what she's going through because he is also a cancer survivor.
Submission (Season 18, Episode 12): The murder case of the week starts when a dog fighting ring is exposed and the finger of a dead woman is found in a deceased dog. Lupo was interested in getting a dog and wanted to adopt one of the dogs rescued from the club, but everybody kept telling him the dogs were too dangerous to reintroduce to society and would be put down. At the end of the episode, we see Lupo taking one of the dogs for a walk in the park, petting him and the dog showing great enthusiasm for his new master. (Truth in Television: The episode was based on the Bad Newz Kennels dog fighting investigation, which sent NFL star Michael Vick and others to federal prison. There was discussion during the case about whether or not the dogs would be safe for adoption. By the time Sports Illustrated released a follow-up on the Bad Newz Kennels dogs six months after the episode aired, almost all of the dogs were successfully rehabilitated and adopted.).
When talking to the girlfriend if a suspect, the woman mentions that she's "500 days sober". Lennie, a recovering alcoholic himself, gives her a brief, but sincere, "All right!"