In "Dear Sis", when Fr. Mulcahy feels that he's useless to the unit. At the end, Hawkeye and the rest of the 4077 let him know just how important he is to them, and sing "Dona Nobis Pacem." Also in the same episode, the look on Major Winchester's face when he opens his Christmas present to see the tobogganing cap he wore as a child—a little piece of home thoughtfully sent for by Mulcahy. Dona nobis pacem.
It's even more heartwarming when you realize that it was actually Radar who sent out for the hat and made it seem like it was Mulcahy's doing, thus helping both the chaplain and the surgeon truly connect to the holiday season.
"Potter's Retirement" has the colonel planning to hang it up after receiving the news that negative reports about his leadership are coming from inside the camp. The party in question turns out to be a mole from a general who holds a grudge against the camp, and after he's revealed we get a scene in Potter's office where Hawkeye, BJ, and Radar let him know how much his leadership is valued and beg him to stay, Hawkeye even addressing him as "Sherman".
In a weird way, the absolute disgust Potter has in his voice when he confronts the mole shows just how protective he is of his men. He's in full Papa Wolf mode there.
As part of a conscious effort by the writers to distance the character of Charles Winchester from that of Frank Burns, Winchester was a part of numerous heartwarming moments over the course of the series, if usually in the episodes' B plots.
The B plot in "Run for the Money". A wounded Private is teased by the other men in his unit and his Sergeant for his stutter, and has been called a dummy for so long that he believes it. Major Winchester rips into the men who make fun of him and tells the Private that he's seen his IQ score and that he's very intelligent, but needs to believe in himself. He then recites a list of famous people who stuttered and sends the Private off with a copy of Moby-Dick, saying that it's fit for a man of his intelligence. He then retires to his tent and listens to a recorded letter from his sister back home...who stutters.
The B plot in "Death Takes a Holiday". Winchester earns the contempt of the rest of the camp by not donating to the Christmas charity drive... because, unbeknownst to them, he is instead following a family tradition of donating a large consignment of confectionery from an upmarket Boston supplier to a local orphanage. He is surprised in the act by the orphanage director, who invites him in to meet the orphans; Winchester declines, saying that the gift must be given anonymously. He later discovers at the camp Christmas party, to which the orphans are also invited, that the director immediately sold the chocolates on the black market, and he confronts the director, only to learn that the money was used to purchase enough rice and cabbage to feed the orphans for a month. He is immediately humbled by the revelation, and returns to the Swamp. Klinger overhears the conversation and follows Winchester to give him a plate of leftover food from the Christmas party... on condition that the gift must be given anonymously. They exchange a "Merry Christmas", addressing each other not as "Klinger" and "Major" but as "Max" and "Charles".
In a weird way, Charles' initial confrontation with the orphanage director was one. Charles, who's usually pretty aloof, looks about two seconds from ripping the man's arm off and beating him with it— and sounds about three seconds into the act.
The B plot of "Sons and Bowlers". Hawkeye's father goes in for surgery Stateside, but the reason for his surgery (which is not identified in the episode) means his survival is not guaranteed. Winchester overhears Hawkeye trying to get through to the hospital where his father is being treated on the camp phone, and proceeds to spend the night keeping vigil with him until they can get word that the elder Dr. Pierce has made it through. As they discuss their relationships with their fathers (a discussion in which we learn that although Charles Winchester II wanted only the best for his son, he was nevertheless a typically emotionally distant patrician patriarch), Winchester calls Pierce fortunate in that while Charles had a father, Hawkeye had a dad.
Hawkeye: Charles, you've never told me anything like this before.
Charles: Actually, Hawkeye...I've never told you anything before.note The only time in the series when Charles sincerely addresses Hawkeye by his nickname.
Actually, it is identified, but Hawkeye only says it once, and his voice is shaking so badly it's hard to understand him. From what I understood, they found a cancerous mass pushing the skin.
The B plot of "Morale Victory". Charles operates on a soldier who had been a pianist until he was wounded in the right hand. Charles, badly shaken by the soldier's despair at his aborted career, remembers that a composer created music which could be played with only one hand, and urges the former pianist not to give up on music, since he still had "the baton, the classroom, the pen. All my life I have wanted to play. I can play the notes, but I cannot make the music." The scene ends with the music being played, one handed.
There's plenty from the finale:
Klinger loving Soon-Li enough to stay in Korea (go back to the early episodes and you'll realize what a surprise that must have been) to help her find her family.
Klinger: I can't believe I'm saying this...I'm staying in Korea!
Hawkeye and BJ giving Potter a respectful, silent salute.
Twice as heartwarming because you can literally count the number of serious salutes that Hawkeye has given anyone throughout the series on one hand.
Potter giving Margaret a kiss on the forehead and hoping that her personal life will be just as good as her professional life.
Potter saying goodbye to Sophie. (Doubles as a Tear Jerker.)
Hawkeye telling BJ "I'll never be able to shake you" and the deep, desperate hug between the two of them right afterwards.
Charles saying goodbye to Margaret. Previously, he had taken back a book of poetry he had given her, much to her disappointment. When it comes time to leave camp, he returns the book to her, now with a written message inside to cover, and kisses her hand, a true Officer and a Gentleman.
Winchester's final departure from the 4077, remaining as dignified as ever, even though he is leaving in a garbage truck. He comments that it's quite appopriate considering he's leaving a dump. He then says his final line, as dignified as when he first appeared.
The "goodbye" stones is a two-fold Crowning Moment of Heartwarming: not only from BJ to Hawkeye (giving him the goodbye that he wanted from BJ and - it's implied - from Trapper), but also from the show to us.
Speaking of Trapper, there's his exchange with Hawkeye when they think he's going home, in "Check-Up":
Hawkeye: Thanks, Trap. Trapper: What? Hawkeye: You made it bearable. I was lucky. You were honest, and open, and let me lean on you. Trapper: (holding back tears) No charge.
Henry's goodbyes to everyone in "Abyssinia, Henry"...before that last O.R. scene shifts everything into full-on Tear Jerker territory.
Speaking of Henry, there's an episode where he's depressed due to not being able to see his newborn son. Near the end of the episode, Radar brings in a Korean woman and her infant son, so Henry could hold the baby for a while. Edges into being a Tear Jerker, as well.
In the "Bug Out" episode, the 4077th is forced to relocate in response to rumors of the encroaching Chinese advance. As part of that, they find an abandoned schoolhouse that they believe is perfect for setting up their army hospital... except that it's already occupied by several Chinese women who are using it as a brothel. After some heated back and forth between the Madam and Colonel Potter, the ladies take an intense interest in Klinger... 's rack of fall gowns. Klinger, for the good of the unit, forfeits the entire rack of gowns, and 'buys' the schoolhouse for them. As Potter commented, "Corporal Klinger, that's the finest act of bravery I've ever witnessed."
Anytime the 4077th get a home movie from their families.
Hawkeye: Henry, if you don't give the order to cry, I will.
The end of the "Rainbow Bridge" episode, where Radar comes to help Hawkeye and Trapper pack for their well-deserved (and much-delayed) R&R in Tokyo. As he works, he turns his back on them and expresses how impressed he is with the work they do, offhandedly adding, "If you ask me, you guys are like supermen." Turning around, he finds them collapsed in exhaustion into their cots...so he quietly covers them up with blankets, whispers, "Goodnight, supermen," and leaves them to sleep.
In "Fallen Idol" Hawkeye hands Radar his Purple Heart medal, and then gives him one of the very few genuine salutes the good Captain ever did.
When Radar is sent home, he leaves behind his beloved teddy bear, indicating both that he is now a man and that he will always be with the unit in spirit.
Any scene during Margaret's transition from antagonist to sympathetic character where she tries to make friends. She suddenly becomes less like a formidable, confidant major and turns into the unpopular kid from middle school. There is one where she awkwardly asks the doctors if she can have coffee with them, then gets really excited when they say yes. The end of "The Nurses" also qualifies.
"Movie Tonight" is an episode full of heartwarming. To start with the entire camp are at each others throats, getting angry over everything. When a move Potter ordered arrives, he gets the entire camp (minus the nurses, who are going to dinner at I-Corp) to meet in the mess tent for the screening. The projector keeps breaking during the movie, and the camp start getting angry again. To stay calm they all sing "Gee, Mom, I Want to Go Home", during which the nurses decided to stay at the camp instead of going to dinner, watch Radar do impressions of famous people, and play the game no one has been waiting for: the Father Mulcahy sound alike contest! When the movie starts playing again, there's a shoot out scene, during which the camp play along and pretend they've been shot and are lying on the ground. An ambulance driver pulls into the camp with wounded and finds them pretending to be dead, and during surgery everyone is singing a song from the movie.
"Preventive Medicine" is one of the darker episodes of the show with BJ and Hawkeye having a screaming fight over whether or not to perform a medically unnecessary operation to get a reckless colonel off the line. Hawkeye does it, compromising his morals as a surgeon, and then it turns out to be all for nothing. Then, at the end, as Hawkeye is sitting alone on his cot in despair, his face in his hands, BJ walks over and places a hand on his friend's shoulder. For a few silent seconds, they grip each other hard before getting up and walking away together. The Heterosexual Life Partners may scream, may crack, may vehemently disagree with eachother, but they still love and stand by one another when needed.
It goes deeper. The argument they had? The views Hawkeye and BJ held were the ones that Alan Alda and Mike Farrel held. That moment they take before they head out to surgery was a bit of a reconciliation between the actors, not just their characters.
Anytime Margaret and Hawkeye have a Friendship Moment. For example, when she tells him she thinks she might be pregnant he is genuinely overjoyed for her and later a bit sorry for her when it turns out she's not pregnant, Hawkeye is the one who comforts her when she breaks down in "Images," and Margaret's divorce is the final straw that inspires Hawkeye to take on the peace talks in "Give Em Hell, Hawkeye." It's really heartwarming to watch them move from deep dislike mingled with grudging respect in the early episodes to a genuinely warm friendship by the end of the show.
There is the classic episode, "Point of View" where we see all the action through the eyes of a soldier and Col. Potter confesses that he feels terrible that he forgot to telephone his wife, Mildred, on their anniversary because he was so busy with a rush of wounded. The soldier tells Hawkeye and the doctor and Radar contact Mildred to explain the situation and she agrees to wait on the line for Sherman, with the instruction that he is to be told that she understands the weight of his duties.
The B Plot of the episode "Dear Mildred" focuses on Radar's attempts to help an injured horse - and hide the horse from Potter. In the end he decides to give the horse to Potter as an anniversary gift. Not only does this ensure that the horse will stay in camp and Radar will get to take care of it, but it also helps Radar to become more at ease around his new commanding officer.
The 4077th coming together to put on a wedding for a South Korean ping-pong champion, including Col. Potter giving the bride away and Margaret helping to sew (or at least alter) the bride's wedding outfit.
In the episode "Where There Is A Will There Is A War," Hawkeye writes out his last will and testament in the event that he is killed. While writing it, he reminisces about his friends and writes out something about each one of them that he loves. The one person he can't seem to find the right words for is BJ, until he has an epiphany and leaves to Erin Hunnicutt a list of all the people her father saved during the war.
It's a bit twisted, but in "Rally Round the Flagg, Boys," a GI is disgruntled that Hawkeye took a wounded North Korean officer ahead of his friend. Throughout the episode, the GI is giving Hawkeye trouble, and a few jokes are made at Hawkeye's expense about how he's short-tempered. The GI finally confronts Hawkeye in his tent, who is reluctant to hurt him for a number of reasons. He's got Hawkeye backed into a corner, when an absolutely furious BJ bursts in and grabs the GI by the shirt. BJ is shaking the man and saying he should break his neck when Hawkeye grabs him to get him to cool off. Shows just how protective BJ can get of his friends.
In "Dear Comrade", the episode is told from the perspective of a North Korean spy posing as Winchester's houseboy, trying to find out how the unit had such a high success rate. The group is so unorthodox and loose he finds it impossible for his faction to replicate it. He does, however, fabricate that he has to stay a little longer, because he'd grown so friendly with the gang, even Winchester - after the spy tells him off for his snobbery and mild racism, Charles just laughs and shows he's Not so Above It All.