How can I keep track of things, in Discworld: Ankh-Morpork?
One of the best ways to see people sneaking up on their victory conditions is to think like them. Here are the win conditions and some tell-tale signs for which victories they might be chasing:


Areas controlled by a majority. This is the most common win condition, so you should always keep an eye on this. It's useful to tot-up after a player's turn when they've gained one or more new majorities.
Areas with a piece present. A great tell-tale sign that the player is Vetinari is that they're placing lots of individual pieces (especially in non-empty areas, where the piece does not give them a majority). Cards that move pieces are also useful for Vetinari who can turn one "controlled" area into two quite subtly.
Money. Chrysoprase needs a lot of money, but don't forget that buildings count as assets (and are harder to lose). Players who buy a lot of buildings tend to be using them to consolidate their money as well as people who just have a huge pile in front of them. A great starting move for Chrysoprase is to try to get an early building that generates money (though that will benefit most players).
Trouble. The Dragon King loves chaos in the streets, so watch out for people who play pieces into territories they have no chance of winning and where trouble would be added. Also, be wary of players who repeatedly discard Watch cards that reduce trouble.
Running out the deck. Vimes can be a tough one to watch, and you shouldn't worry too much about him. The best way to beat Vimes is to win after all! Still, if you want to spot Vimes, you should look out for people who seem happy to tie territories without ever controlling them and players who are discarding and drawing a lot of cards. (Discarding the Time Monks - which shuffles the discard back into the deck - is a great one to watch out for too, because it can vastly increase the "deck size" depending on when it's played and most other players would be happy to play it.)


Lastly a general tip: don't forget that each player has multiple opponents. If you notice that someone might be close to winning with a win condition, especially if they would win at the start of their next turn, don't stay quiet! Let it become the group's problem to stop them from winning instead of just yours.