Alternative Character Interpretation: There is quite a substantial group of fans who hold the view that Carrot is evil and/or The Chessmaster. It helps that he is almost never the POV character - we get to hear what Vimes or Angua think about him but hardly ever see Carrot's actual thoughts.
He has also set up Vetinari Job Security several times: the most obvious is in in The Fifth Elephant when he leaves to pursue Angua and Fred Colon is left in charge, the watch falls apart. Not surprising given that it's Fred Colon, but Vetinari lampshades that as everyone knows Vimes and Carrot will be back soon, no criminals take advantage of the Watchs self destruction for fear of their wrath. The book ends with Carrot very politely bullying the collapsed watch back into shape by reminding them they swore an oath to the king to do their duty.
When Vetinari has trouble reading your motives, says things like, "You drive a hard bargain, Captain," and you reply, "I wasnt aware I was driving a bargain at all, sir," and live you have to be The Chessmaster, albeit probably a benevolent one.
Author Tract: While almost all the books examine real life issues, they usually avoid leaning too heavily onto this trope, informing the stories rather than dictated them, showing rather than telling. Every once in a a while however, Terry's views on religion, race, integration, etc etc etc, take precedence and grind the story to a halt. These moments became a lot more blatant after he was diagnosed with early-onset Alzheimers, as the books in general became much more heavy-handed. Fans overall agree this is the biggest flaw with Terrys writing and some even think it caused Seasonal Rot.
Despite Vimes' almost suicidal urge to be normal in a World Full Of Crazy, he often does things that fall under Refuge in Audacity, such as arresting the military leaders of both Ankh-Morpork and Klatch under charges of Behaviour Likely To Cause A Breach Of The Peace in Jingo.
AE Pessimal. Attacking a troll, of all things, with your teeth is pretty insane, especially when you remember trolls are living rocks.
Pretty much any scene where the Feegles cut loose. Actually, pretty much anything to do with the Feegles, really... They're just that awesome.
Creepy Awesome: Mr. Teatime is sometimes considered to be this - he's extremely creepy, but he's pretty damn awesome as he does it.
Granny Weatherwax started out as a supporting character in Equal Rites, but basically took over the book from the real protagonist by sheer force of awesome and ended up being the focus of the rest of the books set in Lancre.
Same with Vimes and the main Unseen University faculty (Ridcully, Ponder and the Librarian) taking over the Watch series (originally meant to be centered on Carrot) and the Rincewind series.
Genius Bonus: Everywhere. From the fake Latin, to obscure historical and cultural references...
Pratchett uses a lot of physics knowhow, especially with regard to the magic system. For instance, wizards have to deal with conservation of energy when translocating objects, and teleportation requires some very complex calculations. And the blue light that comes off Death's scythe, said to be atoms from the air being split? That really happens. It's called Cherenkov radiation.
Ankh-Morpork's awful cuisine, which is referenced particularly in The Fifth Elephant and Thief of Time, is based on two things: firstly, the pop-culture perception of British food being awful and/or British people making awful chefs, and secondly the very real lineage Britain has of low-quality food and ineffective quality control laws. Think the description of Ankh-Morpork chocolate in Thief of Time is awful? In the real world, underhanded British chocolate companies have tried since the earliest times to swindle customers by cutting their cocoa powder and hot chocolate with things like brick dust and red lead.
Makepeace Thomas Bounder, a cabbage-obsessed, potato-hating poet of awful skill featured in the Almanak, is a round-about Joseph Gwyer, a potato-obsessed poet who was so awful that he was described as the McGonagall of Penge.
Iron Woobie: Despite being the perpetual Buttmonkey, Verence always tries to do his job: be a fool and advisor to his king; an enlightened king to his people; and a husband to Magrat.
Magrat herself has a lot of this, as does Agnes Nitt.
Magnificent Bastard: Lord Havelock Vetinari turned Ankh-Morpork from a broken down, weak city run by a cut-throat, utterly insane monarchy into the most powerful city in the entire Disc, run by a highly efficient government that headed by himself, dominating through cultural and economic might rather than force of arms. Vetinari also happens to be a genius who is the one man who keeps the city in line, knowing without him, it would collapse into chaps, so that none may challenge or remove him. Well aware of how terible the world can be, Vetinari utilizes trickery and manipulation to better it and will happily manipulate other heroes to deal with threats to his city. While Vetinari does not believe a perfect world is even possible, he will scheme, lie, cheat and manipulate all to improve what he can, and is never not in control of events as they unfold.
Stoic Woobie: Without a doubt, Death is the best person for his job, but it clearly takes its toll on him at times, most obviously when he has to collect the souls of his apprentice Mort and daughter Ysabell, at the end of their lifespans.
All graduates of the Guild of Fools are "sad, beaten young men".
This is one of the reasons Magrat is attracted to Verence. He's even more wishy-washy than she is, and that's no mean feat.
Rincewind, who started out as a Jerkass Woobie in The Light Fantastic, has been smacked around by fate hard enough to lose the Jerkass by Interesting Times.
To put that into perspective: The other recurring protagonists of their respective sub-series, Tiffany Aching, Granny Weatherway, Sam Vimes, have year-long periods of happiness between their books. On the other hand, all of Rincewind's books end with him trapped in some hellish place until the start of his next book. The poor guy cannot get a break. The sole exception to this was the end of The Light Fantastic, where he had at least some peace and quiet until the events of Mort (and from there, until Sourcery happened later).
To Rincewind's boundless relief, his life seems to have gotten blissfully boring again in the wake of The Last Hero.
The Bursar just wanted a nice quiet bean-counting job and went librarian-poo dealing with Ridcully.
Otto. William describes thinking of not hiring him as like kicking a puppy.
Mr. Nutt. Of the iron variety. Despite his past and how people treat him when they discover his species, he continually seeks worth and always sees the brightest potential in those around him.
Brick, before Detritus took him under his wing.
Gaspode has his Woobie moments also.
WTH, Casting Agency?: The casting announcements for the BBC series based on The Watch have been contentious at best, with many fans on a scale between "scratching their heads" and "livid." Of particular note, Sgt. Keel is being played by a black man — despite the books making it a plot point that he and Vimes look alike. Vetinari, CMOT Dibbler, Doctor Cruces and Lupin Wonse have all been gender swapped. And Sybil Ramkin, described in the books as an older, rotund, white woman, has been cast as a young, attractive black woman. About the only casting decisions fans seem to agree with are for Vimes and Carrot. Fans are particularly baffled after the spot-on casting of other Pratchett adaptations, like Good Omens (2019) and Hogfather.