These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Anvilicious: Death's speech to Susan about how humans need fantasies like the Hogfather (i.e. Santa Claus), or Terry Pratchett's books for example, to believe in when they're young so that when they grow up, they can believe in big fantasies like justice, mercy and...purpose. Depending on your perspective, this may even approach Broken Aesop territory, given its potential for Unfortunate Implications. On the other hand, this is the Discworld, and Your Mind Makes It Real is an actual law of nature. The fantasies do become real... so if something that that's not a physical inevitability- like justice, say- is sincerely believed in... if you're confining it to the Discworld, that's pretty positive.
Besides which, the point was that something doesn't have to be a concrete idea to be a valid one.
Complete Monster: Jonathan Teatime. Lord Downey let him into the Assassin’s Guild out of pity that his parents died only to suspect that he killed them. If he is sent to kill someone, he will mercilessly slaughter them, their family, and their pets. He kills any accomplices he has the instant they're not currently useful to him, not excepting Ankh-Morpork's most gifted lock-picker who was an incredibly valuable asset to the Guild. He horrifies even hardened criminals who’ve earned their reputation on murder. The most terrifying thing about him is that he honestly doesn't understand that his sadistic behavior is wrong. He sees no difference between having a friendly chat with a man and stabbing him to death
Ensemble Darkhorse: Teatime is quite the popular character among fans, despite only appearing in this one book.
Fridge Logic: Violet the tooth fairy girl and Bilious the Oh God of Hangovers are attracted to each other. Violet compounds the Oh God's attraction by mentioning she's part of a temperance movement and doesn't drink. Where does Susan know Violet from? They've seen each other at Biers, a pub ...
Biers serves a rather ecclectic clientelle, and it makes sense that not all the drinks there are alcoholic (or edible by human standards for that matter). Angua goes there and orders fruit juice in Feet of Clay.
For that matter, as Biers appears to be the only main centre of nightlife for the aforementioned eccentric clientele, it's entirely probable Violet only goes for the company or possibly the food.
Genius Bonus: Many of the computer references made towards Hex. In particular the teddy bear being removed might be a reference to the Microsoft Teddy Bear which was used as the icon for a vital file in the early windows OSs. Many users (helped by an email hoax) mistook the strange file for a virus and deleted it, with disastrous consequences.
Nightmare Retardant: In-universe. Gawain and Twyla don't find Death scary, thus not identifying him as a "monster", partially because he's on a big comfy chair and eating a biscuit.
Uncanny Valley: The kids find Teatime's freaky heterochromia is a great deal scarier than a talking skeleton. Particularly because, as mentioned above, the skeleton is sitting in a comfy chair and eating a biscuit, and because Mr. Teatime's speech and mannerisms are never quite natural.
Poor Bilious. Sure, we don't feel quite as sorry for him as we do for, say, Rincewind, but the poor guy gets all the hangovers from the god of wine without ever getting to actually enjoy earning them.
There is a chance that since adult concepts such as death do not exist in the Tooth Fairy's world, then hangovers might not exist either.
The Cheerful Fairy. The Senior Wrangler, at least, falls for her because of her Woobie-ness. Then he becomes a Woobie when she vanishes just before he was about to get serious with her.
Iron Woobie: Death. A recurring theme from his own Myth Arc, true, but it's especially visible when you see just how much he prefers giving presents to the living instead of guiding the dead.
Can't Un Hear It: Regardless of your opinion on the TV adaptation, Michelle Dockery and Marc Warren's performances as, respectively, Susan Sto Helit and Jonathan Teatime are probably going to be definitive.