The tearful conversation between Banagher and his dying father when he entrusts the Gundam Unicorn to him.
When Daguza indirectly admits that he considers Banagher as a surrogate son, and goes out of his way to help him deal with his emotional problems.
Marida and Banagher's conversation in the sick bay, in which she begs him to not abandon his integrity and personality.
Nameless pilots shine bright in this series. A nameless Zee Zulu pulls a Heroic Sacrifice to save his fellow pilot from the Byarlant Custom that's been massacring them.
Banagher's and Audrey's reunion in Episode 5, and Zinnerman and Marida's reunion shortly afterwards.
Alberto's concern for Marida throughout Episode 5.
Save for a few framed commendations and pictures, Bright's office aboard the Ra Cailum doesn't stand out. But it's what's in the photos that's heartwarming: one on his desk (which is presumably his wife and kids) and a wall portrait of Amuro that doubles as a Tearjerker. Amuro is wearing the same outfit he wore on Londenion in Char's Counterattack, which means the picture was taken only days (at best, weeks) before Amuro was killed in action. In the next episode, Bright even speaks to the photo fondly. Considering that the two didn't exactly hit it off when they first met, the fact that they became close enough for Bright to include Amuro amongst the photos of his family is touching.
This remarkably quiet scene from Episode 4 where Audrey has a conversation with an old diner owner on Earth, which can double as a Tearjerker. Through the ensuing conversation, Audrey (and the audience) gets to see how things look from an Earthnoid's perspective. The Federation's whole space program was originally intended to be a temporary measure to help the Earth recover, which at least a sizable portion its citizens willingly agreed to pursue. Until Spacenoid resentment, Zeon, the One Year War and ultimately Char's Neo-Zeon shattered the progress being made. The irony of it all is that despite everything, even the best of intentions devolved into hatred, with humanity still having no answer. But its shows that even with bloodshed, the man still believes in the hopes and dreams his forefathers placed in the Universal Century.
In Episode 4, Banagher and Zinnerman are having a conversation in the desert about the ways of the Universal Century. Banagher begins to cry at the sadness of it all. Zinnerman begins to speak, causing a distraught Banagher to mumble "I know, I know... you're gonna tell me that a man doesn't cry in front of others." Zinnerman's immediate response is a quiet, gentle "no." Banagher looks up, wide-eyed and confused and Zinnerman delivers an immortal line: "Crying because you care is an entirely different matter. I don't trust anyone who never cries. That's my philosophy." Banagher breaks and begins sobbing freely.
Episode 6. "Father... Just this once, will you let me have my way?" Also doubles as a Tear Jerker.
In Episode 7, when Laplace's Box is finally opened, Martha realizes the Vist Foundation is done for. However, Alberto calmly says that even without the Box, they can always start over. Martha gives her nephew a genuinely motherly smile before being led away by Bright's men.
It's also revealed that Cardeas Vist never wanted Banagher to pilot the Unicorn in the first place, though he would have been proud of what was accomplished.
At the conclusion of Episode 7, Captain Otto invites Captain Zinnerman out for a drink once everything is over; he even salutes the latter, which Zinnerman replies with a proper salute of his own. Remember that these two men used to be mortal enemies.
And after that, the ECOAS operator who gives a friendly wave to Zinnerman and his crew, showing how the Nahel Argama and Garencieres crews have become Fire-Forged Friends.
Banagher nearly ascending to a higher plane of existence as a perfected Newtype, before remembering his promise to Mineva to come back alive.
Riddhe was the one who reminded Banagher of his promise, even though he is in love with Mineva/Audrey himself.
And also the ghost of Cardeas Vist appearing to stop Banagher from ascending and pointing him to where he SHOULD be going. Back to Mineva.
In Episode 7, we briefly see the spirits of Amuro, Char and Lalah coming together and talking like old friends.
The Reveal in the One Hundred Years of Solitude miniepisode that the ghost of Cardeas Vist was with Syam the entire time, implying that he was also there to see Banagher.