1) The keeping of the peace and the rule of law are not to be sniffed at. Getting inside the head of Sam Vimes (Vimes is brave; Vimes is obstinate; Vimes is put-upon; Vimes is grouchy and ill-tempered in a way which is really a kind of grim good humour; posh people make Vimes's skin crawl; Vimes is a hugely reluctant social climber; Vimes struggles with his old-fashioned bigotry and sexism; Vimes doesn't have to be an idealist or a realist because he's just always a bit knurd; on some level Vimes is probably a bit overwrought that he has never quite had to sacrifice his life for the greater good; Vimes is prone to inner conflicts between an id-like "Beast" and a superego-like "Watchman"; Vimes is exactly the person you want with you in a tight corner; Vimes is (sorry) bae) is an excellent way not to sniff at them.
2) Nor should we forget the angle at which Pratchett first came in on the City Watch, imparting a general orientation to everything which followed. In the rhetoric of TV Tropes, these police started out as genre-savvy mooks (or redshirts, perhaps: and cf. e.g. John Scalzi's Redshirts, and the massacred henchmen of Austin Powers).
That is: one of the running themes of Guards! Guards! is the way in which stories treat certain minor characters as disposable, just to show off the swordplay and other heroic antics of the major characters. But here are characters who don't feel "minor" and who refuse to be disposable.
I really like, by the way, guessing at the shifting nuance of these translations of that excellent title. Look especially at the Italian, the Norwegian/Swedish, and at the Spanish:
Стражите! Стражите! (Bulgarian)
Stráže! Stráže! (Czech)
Wacht! Wacht! (Dutch)
Vahid! Vahid! (Estonian)
Vartijat, hoi! (Finnish)
Au Guet ! (French)
Wachen! Wachen! (German)
שומרים! שומרים! (Shomrim! Shomrim!) (Hebrew)
Őrség! Őrség! (Hungarian)
A me le guardie! (Italian)
I lovens navn! (In the name of the law) (Norwegian)
Straż! Straż! (Polish)
Guardas! Guardas! (Portuguese - Brazil)
Gărzi! Gărzi! (Romanian)
Стража! Стража! (Russian)
Straža! Straža! (Serbian)
¡Guardias! ¿Guardias? (Spanish)
I lagens namn (In the name of the law) (Swedish)
3) Nor should we forget that what is fantastical about the City Watch isn't exactly that it includes dwarves and werewolves and vampires and trolls and so on in its ranks -- Captain Carrot Ironfoundersson, Captain Angua von Überwald, Lance-Constable Salacia "Sally" von Humpeding, Sergeant Detritus, Sergeant Fred Colon, Corporal Nobby Nobbs, Sergeant Cheery Littlebottom, Constable Reginald Shoe, Inspector A. E. Pessimal, Constable Igor et al., hi guys <3 -- which is really less extraordinary than the idea that the Watch is roughly representative, in many different ways (see note), of the population it polices.
The Watch is not an elite fraternity of mostly financially flourishing white men, whose individual kindnesses and cruelties mostly cancel out (as in the expression "oh, it'll all come out in the Watch"), leaving only their Job, and who will, if you try too energetically to advance a Vimesian agenda of peace, order, pragmatism, mild cosmopolitanism and substantive legal equality, come up to you and wound you, because that's their Job. Guard labour! Guard labour! In other words, there is an element of utopianism to the Watch -- or at least of a weirdly inverted satire -- since half the time it is the Watch's virtues, not its vices, that are grotesquely amplified and enlarged compared with Roundworld correlates.
4) But. Although the Watch sequence is interested in exploring the space between the voice that shouts "Guards! Guards!" and the voice that shouts "Police! Police!", it frequently finds that space to be unexpectedly cramped.
I think there is an intermittent discomfort with the whole idea of taking a police perspective in the first place, a restlessness which finds expression in many ways. The novel Night Watch is perhaps one big example, in which a time travel conceit lets Pratchett just park that liberal progress shtick, and stick his copper on top of a barricade in pitched battle against a repressive state.
But I also just noticed a small example in Thud!, which was really all I want to point out here. "Pig" is, of course, a way of referring to a police officer when you don't want to hear any excuses. It's a way of saying, "Because all humans, despite and because of our sublime diversity, are in some fundamental and important sense equal, the only truly inhuman thing anyone can do is a Job which wages endless war on that equality." It's a way of saying, "Become human again." It's a way of saying, "Quit."
It can be a way of saying, "Die," although this can also depend on things like vegetarianism.
In Thud! Vimes is, in two separate ways, associated with not the pig, but with the ambivalent figure of the pig-not-pig. A kind of Schrödinger's Pig.
The first is, of course, the "BLT" sandwiches with which Vimes hopes to evade Lady Sybil's health regime, and which contain either superabundant bacon and negligible garnish, or jungles of lettuce and tomato and next-to-zero bacon.
The second has a direct link with finance. It sees Vimes encircled by a spectres of frozen, temporally inverted pig meat. Vimes visits the Pork Futures Warehouse:
The Pork Futures Warehouse was one of those things, the sort that you get in a city that has lived with magic for too long. The occult reasoning, if such it could be called, was this: pork was an important commodity in the city. Future pork, possibly even pork as yet unborn, was routinely traded by the merchants. Therefore, it had to exist somewhere. And the Pork Futures Warehouse came into existence, icy cold within as the pork drifted backwards in time.
* * *
Note: Btw & fwiw: there's a fairly strong sociologically working class vibe in Vimes's Watch. How do their finances stack up? Setting aside the fact that the Discworld hasn't been pedantically worldbuilt in advance, and various mentions of salaries and prices don't always seem to quite fit together: if a Watchman gets $30 a month, then using the 50c-per-day rate for stable hands mentioned in The Truth as an analogue for the UK minimum wage, that would give us a back-of-the-envelope Watchman's salary of around £26,000, very close to the actual starting police officer salary in my part of Roundworld (although not counting overtime bonuses, which can be enormous: ultimately the Job is compensated at more-or-less the same level as dentists, accountants, and civil engineers, and a bit below architects, lawyers, and the lower tiers of finance professionals).