Marty's relationship with his ancestors is pretty heartwarming. Seamus quickly becomes protective of the "strange young man", though he doesn't know why he feels that it's important for him and Maggie to help him, not knowing that he's their great-great-grandson. And Seamus impacts Marty, as Marty finally realizes that you don't always have to prove yourself to others to affirm your masculinity or pride.
Seamus and Maggie are Irish immigrants in the American West. It's a challenging life even by 1885 standards, but one senses their joy and accomplishment in being pioneers in their new country, especially as Maggie describes William (Marty's great-grandfather) as being the first McFly to be born in America. The scene where Seamus cradles William by the hearth is beautifully executed.
As Marty is leaving to catch the train, he shouts for Seamus to "take care of that baby."
It can be argued that Seamus changed Marty's entire future - Marty refuses to race Needles at the end of the movie thanks to his new mindset, which led to his bleak future as we see in Back to the Future Part II. An interesting inversion of Marty being the one to change other peoples' futures in Part 1.
After the whirlwind ride of the first and second films as well as the intro of the third, we get Marty carrying 1955 Doc home after he passes out, followed by the two of them lying in two exhausted heaps in 1955 Doc's living room on a stormy Sunday morning. 1955 Doc has had a rough week inventing Time Travel, helping Marty guarantee his future existence as well as getting him back to 1985 in the first film. Marty had just saved his dad and rescued his family from Biff and generally saved the world along with 1985 Doc in the second film, and also brought the unconscious 1955 Doc home. They were literally superheroes in their own right (laying aside that it was mostly their time-traveling that caused much of the mayhem), but now they're just two regular guys getting the break we all know they damn well deserve. The harp music helps sell the scene.
1985 Doc's letter, especially considering that he intended it to be his last-ever words to Marty. It's even recognized as heartwarming such In-Universe.
And so, Marty, I now say farewell and wish you godspeed. You've been a good, kind, and loyal friend to me. You've made a real difference in my life. I will always treasure our relationship and think on you with fond memories, warm feelings, and a special place in my heart. Your friend in time, "Doc" Emmett L. Brown, September 1st, 1885.
Although 1985 Doc asks Marty in the letter to respect his desire to remain in 1885 and not to come get him, Marty has to disregard that request. Why? Because he spots his friend's tombstone in the cemetery, revealing that he was killed by Buford "Mad Dog" Tannen shortly after writing the letter. But rather than despairing about it, Marty is firm in his resolve to set things right.
Marty:[to 1955 Doc] It's not gonna happen, Doc. After you fix the time circuits and put new tires in the DeLorean, I'm going back to 1885 and I'm bringing you home!
Speaking of the tombstone, it goes from having Emmet Brown's name to Clint Eastwood's name. Then Buford breaks it, which could have changed the shape of the tombstone, but instead erases it from existence, meaning that plot was never filled. Nobody died that day.
When Marty starts to beat himself up over 1985 Doc getting stuck in 1885, 1955 Doc makes a point to assuage his guilt by pointing out he could've wound up somewhere worse than the Old West.
There's something quite endearing about 1955 Doc, a guy who's literally a genius, helping Marty read the word "schematics" without commenting on the latter's intelligence. Even if 1955 Doc already knows Marty is highly intelligentnote given that he managed to connect his video camera to 1955 Doc's television set, he could have chosen to lord his even greater intelligence over him. Nope. No Insufferable Genius here.
In the novel, 1955 Doc offers to let Marty not go through with the rescue plan when he sees how unsure that he's going to succeed. Marty immediately rejects this, and says that since he got Doc into this mess, he's going to get him out of it.
1955 Doc's last scene in the BTTF trilogy is him seeing Marty off with a gunshot in the air and a "Happy trails, Marty! Vaya con dios!"
Even better: the first time around, Doc likely didn't see the DeLorean returning in its full glory, as he was knocked to the ground and turned only to see the DeLorean gone and it's fire trails down the road. The second time around, Doc gets to see his time vehicle with no such distractions. He finally gets to see something he built work.
1985 Doc's reaction to seeing Marty in 1885. He could keep up his facade of being displeased with Marty for all of a few seconds.
Doc: Marty, I gave you explicit instructions not to come here but to go directly back to 1985.
Marty:(gasping for air) I know, Doc. But I had to come.
The novelization adds a little more heartwarming to it by pointing out that Doc didn't realize how much he missed his own time and friends until he saw Marty about to be hung.
This film is the first time in Marty's time traveling career when he isn't roped into time travel by the Doc or forced by circumstances to save his own skin. Marty takes it up on himself to save his friend even if Doc Brown in 1955 wouldn't have blamed him if he just stuck to the plan to go back to 1985.
After Doc brings Clara back to her house, he accidentally reveals in conversation that he's a scientist (rather than a blacksmith as he's known around town). Clara perks up when she hears this slip-up, and immediately asks what kind of scientist he is, showing that she has more than a passing appreciation for the sciences just as he does.
Doc and Clara at the telescope.
Clara: I think the lens may be out of alignment, because if you move it this way, the image turns fuzzy, see? [moves closer to Doc] But if you turn it... the other way...
Doc:[gazing at Clara] ...everything becomes... clear.
The two of them gush over their shared love of Jules Verne when Clara finishes his quote from From the Earth to the Moon. Then, when Doc almost blows his cover by saying that he read 20,000 Leagues Under the Sea when he was a boy, which Clara points out had only been published ten years prior in 1885, he covers it up by saying that it made him feel like a boy, which is an even sweeter implication.
Doc adorkably trying to ask Clara if she wants to dance, "Would you like to... I mean, would you care to...", to which Clara simply says "I'd love to."
The final scene of the trilogy, in which Doc and his clan travel from the 1890s to 1985 to visit Marty and Jennifer. Highlights include Doc giving Marty the photo of themselves with the clock, and of course:
Jennifer: Dr. Brown, I brought this note back from the future, and now it's erased.
Especially so because it negates some of the bitterness of the Bittersweet Ending the film seemed to be setting itself up for (Marty succeeded in saving Doc; he's found love and he's happy in the past, but they'll never see each other again). Whatever you want to believe follows from here, the "Partners in Time" do have the ability to keep up with each other.
Better still, that speech sums up the core of the series. Nothing is set in stone. George could have become a wimp in a hopeless marriage, or he could stand up for himself and let his future wife know how much he loved her. Marty could have destroyed his dreams defending himself against every insult he received or he could grow beyond it into a bright and promising future. A little sweeter is that it's Doc who's delivering this speech. He could've given up after being called a crackpot or bowed to his father's wishes, but he went on to invent the time machine in every timeline he could. As he said in the first movie, and said first (sort of; Jennifer credits him), "If you put your mind to it, you can accomplish anything."
On the train, Clara just happens to be sitting in front of the salesman that Doc was speaking with at the bar, who's recalling Doc's conversation with him about her, and she overhears her name.
Clara: Excuse me.
Salesman: Ma'am.
Clara: But was this man tall, with great big brown puppy dog eyes and long silvery flowing hair?
Salesman:[surprised] You know him.
Clara:[sighing] Emmett!
The fact that she can recall such details really shows how much they loved each other. Especially considering most people describe Doc in far less flattering terms ("Crazy, wild-eyed old man," anyone?).
In the novel, the salesman doesn't react to her obviously over-romantic description with scorn or derision, but earnestly urges Clara to return to Doc when he recalls how heartbroken Doc was.
The scene where Marty goes to get his truck, Biff comes out of nowhere, not knowing it's Marty (he's wearing his "Clint Eastwood" outfit) at first because he thought someone was gonna steal Marty's truck. He of course reverts back to his "Nice Biff" persona when he is mistaken, but the gesture itself is pretty heartwarming.
Even if Biff is only nice around Marty and his family, seeing him all submissive feels like a refreshing departure from 1985-A Biff. 1985-B Biff is a relieving indication that everything is as it should be.
Also, the fact that even though Marty has every reason to treat 1985-B Biff with as much hostility as 1985-A Biff deserved (and Marty probably had it to here with Tannens at that point), he proves to be the bigger man and treats 1985-B Biff with only the bare minimum assertiveness.
Just seeing Marty reunite with his family in 1985! After seeing their unhappy existence in 1985-A, it's so touching to see the McFlys all safe and sound. George is alive, Lorraine is married to him, and Dave and Linda are fine. It's one thing to see Marty and Doc fix the timeline, but here, we get to see it come to fruition. All is right with the world once more.
Marty finally being reunited with Jennifer near the end of the movie, after worrying about leaving her in 1985-A in Part II. The way he gently wakes her up, and her relief when she says "Marty!" as they hug (considering that the last time she saw him, he was an older, broken man who had completely changed from the boyfriend she knew) is really sweet.
Not to mention that they actually got their kiss without interruption. For once.
When Buford tries to lure Marty out for their gunfight by threatening to shoot Doc instead, Doc yells at his friend to stay away and save himself.
The clock tower plays just as important a role in the series as the DeLorean itself. Since Marty and Doc wind up being on hand to see when it stops working, it's only fitting that they be on hand to see the clock activated for the first time. Doc even comments on it. Then they get their picture taken next to it, despite the fact that they won't be able to show it to anyone.
Marty teasing Doc about his "girlfriend" Clara, whose name appeared on his tombstone ("erected in eternal memory by his beloved Clara") but whom he hasn't even met yet. He's only got a week to meet her before he either gets shot dead by Buford or returns to the future in the DeLorean.
Doc: Marty, it's impossible. The idea that I could fall in Love at First Sight? It's romantic nonsense. There's no scientific rationale to that.
Marty:[Laughing] C'mon, Doc, it's not science. You meet the right girl, it just hits ya; it's like lightning.
Marty: That's the way it was for me and Jennifer. Man, we couldn't keep our eyes off each other!
After losing Clara, the Doc goes to drown his sorrows at the local saloon, and is there all night until Marty arrives to try and convince him to come back to the future. Doc, probably realising that there isn't really anything left for him in 1885 and he'll be miserable if he stays, immediately perks up and agrees to go back to 1985. Marty basically came to cheer up his best friend after a bad breakup.
The locomotive sequence:
Clara is on the train yelling to Doc. When he finally notices her, she yells "I love you!" like an awkward schoolgirl confessing her first crush.
Then it cuts back to Doc, who was nervously climbing across the locomotive only moments before, and he has this look of utter joy on his face.
The shot of Doc and Clara riding off into the sunset on Marty's hoverboard from 2015, with Doc holding her in a Bridal Carry and zipping away from the soon-to-be time-traveling DeLorean and soon-to-be-doomed locomotive.
In a more general way, Doc's entirely successful life in 1885 Hill Valley prior to Marty's arrival. In his own time, people think he's a dangerous nutjob living in a crappy garage with only a chain-link fence separating his property from the dumpsters of a Burger King. His reputation is so bad that Principal Strickland actively discourages Marty, Doc's only known friend, from hanging out with him (you'd think if Strickland were really concerned for Marty as a student, he'd be okay with him spending time with a literal scientist). He owns a "24-Hour Scientific Services" business, but what the hell is that? He's even allergic to synthetic fabrics! Meanwhile, in 1885, he's respected in the community, his work as a blacksmith is important and lucrative; several scenes imply that he's actually pretty popular among his neighbors, and he actually gets to be a fairly snappy dresser because synthetic fabrics aren't a thing yet. He achieves all this in a matter of months. Knowing all the shit he's had to deal with over the course of his life, it's so nice to see people appreciate him.
It also explains why he was perfectly fine staying in the past.
In 1955, when Doc and Marty retrieve the time machine from the mine, the dog Copernicus is the one who finds Doc Brown's 1885 grave and sets the entire process of rescuing Doc from the past in motion before he can be murdered. Copernicus knows his master's scent even though he's been buried for over 70 years, senses that something is definitely not right, and stays at the grave until Marty comes over to see what's wrong.
After Marty convinces Doc to return back to 1985 with him, the latter wishes to at least say goodbye to Clara before leaving. He avoids giving any details as to where he's going, unwilling to alter time any further - until she pleads to him that if he truly loves her, he'll tell her the truth. Without even a second of hesitation, Doc immediately obliges.
Why does Doc return to 1985 once he's able to build the Time Machine Train? To see his best friend and tell him he's alright and retrieve his loyal dog, Einstein.
There's also something really sweet about Marty and Clara's reunion during the final scene. They only knew each other for a few days, yet Clara saw how much Doc and Marty cared about each other. It's not hard to imagine Doc's told his wife all kinds of stories about his Partner in Time in the years between the last 1885 scene and the Time Train's jump forward. So Clara's delighted to be reunited with her husband's best friend (and the feeling's reciprocated by Marty).
