The shocking reveal as to how Samuel Vimes spent his money before becoming rich. He donated about half his monthly earnings to the widows and orphans left behind by dead watchmen. At the end, he'll probably give it up since Carrot gets Vetinari to approve of pensions for widows.
Cuddy teaching Detritus to count. Aww.
Just the discovery that Detritus isn't as stupid as people think he is, and the enthusiasm Cuddy has when teaching him to count strikes chords with anyone who has ever worked with a kid and discovered that same thing.
Later, he saves Detritus from freezing to death. And goes to Quarry Lane to - hopefully - find a troll doctor. And then he threatens other dwarfs for throwing an axe at Detritus.
Detritus's reaction to Cuddy's death. Made all the stronger by Carrot talking him down from obliterating a whole room's worth of assassins shortly afterwards.
"They call me Mister Vimes."
When Gaspode refuses to leave a distraught Angua even when she's growling what's implied to be Canine for "Go away or I'll rip out your jugular".