There is a subtle one at the very beginning of the book. After Carrot tells him Stronginthearm was murdered after signing off, Vimes states that he died while on duty because that means Stronginthearm's parents will get a bigger pension. Vimes and Carrot, possibly the two most lawful and rule-abiding characters in the whole of the series, falsify a report without a moment's hesitation in order to provide for the family of a dead copper.
This fully in character with both of them, all the way back to the early Watch books. In Men at Arms, Vimes was supporting the widows and children of fallen Watchmen from his own meager pay - this was before he'd married Sibyl or gained any kind of wealth - and Carrot either knew about it already or recognized the names instantly when Angua found the list, even though most of them must have died before he joined the Watch.
The whole scene at the cemetery at the beginning. Or perhaps it's more of a Tear Jerker. But it's definitely a heartwarming moment when Vetinari turns around and has a lilac sprig on his robe, and then casually mentions that he's going to "explain matters" to the new deacon. Not explained at that moment at all, but try reading it again. And mind you, that was before the history changed, so Vetinari must have reacted the same way to Keel's Last Stand or whatever it was in the original timeline.
Sergeant Colon's uncharacteristic show of honest anger at Corporal Ping's question about wearing a lilac is both pretty cool and this when you realize there's very few times Colon has come close to losing his temper or hitting someone throughout the series. What cements this though is Nobby's call for Fred to steady himself and then subsequent moment of anger at Ping's question of where they were going.
"Anyone important enough to ask where we're going—"
"—knows where we've gone!"
Vetinari's comparatively short explanation at the end. Doubles as Moment of Awesome for him, I guess. He just saw it happen, and he just joined in. Took no particular pride in that.
"I saw a man called Carcer... vanish. And I saw a man called John Keel die. At least, I saw him dead."
"Really," said Vimes.
"I joined the fight. I snatched up a lilac bloom from a fallen man and, I have to say, held it in my mouth. I'd like to think I made some difference; I certainly killed four men, although I take no particular pride in that. They were thugs, bullies. No real skill."
Vimes's speech to Vetinari at the end ("How dare you? How dare you! At this time! In this place! They did the job they didn't have to do, and they died doing it, and you can't give them anything. Do you understand?"), after he captures Carcer, who had been taunting him the entire book.
Vimes in the graveyard reflecting on the revolution and coming to the conclusion that "he was honored to have been there twice."
The engraved cigar case arriving.
The birth of Sam Vimes Jr. Immediately followed by Vimes falling to the floor, asleep, after spending days awake in the past.
"I'll teach him to walk! I'm good at teaching people to walk!"
Reg Shoe's annual gesture of solidarity. Eight good men died at Treacle Mine Road: he was the only one to rise from the grave. So every year, on that anniversary, he goes to his empty grave in that little graveyard and lies there with them.
This is especially heartwarming, because normally Reg is trying to get the dead to come out of their graves, making speeches at graveyards, putting fliers in coffins, and has had two complaints filed against him since he joined the Watch for these activities.
Just before the big fight. Every single watchman stayed with him, despite knowing that the odds were heavily against them.
The ending, just after the graveyard scene and Vimes's rant to Vetinari.
"And then he went home. And the world turned toward morning."
Some of Vimes' interactions with his young self indicate just how much he's grown. Particularly when Vimes forgets the torturer he's tied up in the basement until they light the building on fire; younger Vimes thinks he's done it on purpose and relishes the notion of such an evil man burning to death. Vimes runs into the building to rescue the man, or at least give him a chance to escape. It fits in perfectly with Vimes' struggles to control "The Beast" and to keep to the law, at least as far as is pragmatically possible.
Moments of camaraderie between Vimes, Colon, and Nobby in previous books become Heartwarming in Hindsight after seeing just how long they've known each other and how much they've been through together.
Vimes/Keel: I mean, how long have I known you, Fred [Colon]? Colon: Two or three days, sir. Vimes/Keel: Er... right. Yeah. Of course. Seems longer.
The Book and the Watch Series as a whole closing a circle:
Anton's friendship with his vampire neighbours in The Night Watch. Once he gets over the initial shock of finding out the nice family next door are vampires after he becomes an Other, he decides, in true Anton Gorodetsky fashion, to say screw you to Fantastic Racism and invites them for tea, eventually becoming a Big Brother Mentor to young Kostya. Too bad this all goes horribly, horribly wrong...