While any dialogue concerning the Unseen U's senior faculty can be considered, this one stands out. It starts out with the Dean saying the Librarian isn't a proper orangutan, not having the huge cheek pads a dominant male should. Later on, it is pointed out that while the Librarian is the only orangutan at UU, he's only the librarian, and doesn't dominate the University.
One by one, as the thought sank in, they [the faculty] grinned at the Archchancellor. Ridcully: Don't look at my cheeks like that! I don't dominate anybody!
Ponder explaining to Rincewind that "We're wizards, you know. We could give you your own bag of wind."
Ridcully: Ah. Forward the Dean.
The Dean: I heard that!
Ridcully's attempt to send The Dean to the counterweight continent:
The Dean: But I hate foreigners!
Ridcully: So do they. You'll get along famously.
Every staff member claiming to have visited their aunts in distant towns during the events of Sourcery...except Ridcully, who really had been in a distant area at the time.
Then there's the faculty's reaction to The Luggage. Of note, the Dean somehow got into the chandelier, much to the Librarian's annoyance.
Ridcully's reason for wanting to send the Dean; "They asked for the Great Wizard, Dean, and I thought of you." ...because he's the only man who can sit in two chairs at the same time.
A fact illustrating the unreliability of magic armour: the last words of many of the Disc's ancient lords were "You can't kill me because I've got magicaaargh."
Rincewind getting comfortable with the Red Army controls.
"There are not 2,300,009 invisible bloodsucking vampire ghosts."
The wizards kill Hong by teleporting a lit cannon right next to him. Accidentally.
And thinking they were doing the Agateans a favor by lighting it first, mistaking it for a harmless firework. Well, they were doing them a favor, just not the one they thought...
The scene where Lord Hong admires himself, dressed up in Ankh-Morpork nobleman's fashion and envisions himself receiving the admiration of the Morporkians. The actual reaction of them, the text notes, would be more like "'Ere wot a toff! 'Eave arf a brick at 'im!"
The entire footnote involving how to scream for mercy in other languages, and the ensuing running gag throughout the rest of the book.
The Samurai warriors perform the old trick of slicing silk kerchiefs as they fall. Cohen tosses his own, admittedly more used, hanky in the air. While the Samurai are watching the hanky keenly, Cohen takes the opportunity to decapitate them. Age and treachery scores yet another triumph over youth and skill.