Just as Vimes and Carrot arrive on the scene of a recent riot, he says:
Vimes: It's over. You can tell by the sudden increase in suspiciously innocent bystanders.
Every time Vimes uses the word 'Vet' when talking to Angua's parents.
Similarly, every time he uses the word 'Bath'. Or 'Bad' which means bath in German and has the Bad Dog implication in Engli... er, Morporkian.
This exchange - which suggests, by the way, that Sam Vimes may be a not entirely unappetizing sight out of uniform.
First Gloomy Sister: Have you come here to ravish us? Vimes: Madam! I am being chased by werewolves! Second Gloomy Sister: Vill that take all day?
On his Wikipedia page, he looks reminiscent of Clint Eastwood. Plus, at the time, he's wearing only half-frozen underpants.
In Where's My Cow Vimes is referenced from Pete Postlethwaite, which is who Pterry says he imagines him looking like.
If you're a fan of Chekov, the whole exchange with the sisters is screamingly funny.
"Vimes took in the good but old clothes, the faded gentility, and played the only card in his hand. 'I am His Grace the Duke of Ankh-Morpork,' he said, 'Although I realize that fact is not apparent in my present circumstances.'"
When acting captain Colon realises what a mess he made of things (i.e. he's the only one in the Watch, the rest of the watchmen formed their own guild and are currently on strike)
Mister Vimes is going to go completely bursar. He's going to go totally Librarian-poo.
Sam's reaction to The Reveal of what Sybil has been trying to tell him but continually getting interrupted. Rarely if ever do we see Vimes so completely flabbergasted in canon.
Immediately followed by him telling her to barricade herself in their room (as there are werewolves after them), and adding, "Without straining yourself!"
When Sybil finally tells him that she's going to have a baby, he's only half-listening, and very nearly responds with something like 'Choose any color you like' or 'I'll have some men come by in the morning and sort it out.' Probably a good thing that he managed to do a double-take before going with either of those responses.
Sergeant Detritus, Cultural Attache.
The gloomy and purposeless trousers of Uncle Vanya (which is also a Shout Out).
Vimes being plucked from the brink of death-by-werewolves when Carrot, wielding a spear, appears in a sleigh, extremely abruptly, to the point where for three paragraphs in a row all Vimes can do is say "Carrot?" before he finally manages "What the hell are you doing here?" Carrot's total nonchalance is just icing.