Carrot has enlisted Gaspode's help to track Angua. Gaspode is the flea-bitten talking wonder-dog that you may recall from earlier books.
From page 25:
'Do you know anything about this?' [Vetinari] said.
Vimes read, in large, round, crayoned letters:
'DeEr Cur, The CruELt to HOMLIss DoGs In thIs CITy Is A DIssGrays, WaT arE The WaTCH DoIng A BouT IT¿ SiNeD The LeAK AgyANsct CrUleT To DoGs.'
'Not a thing,' he said.
'My clerks say that one like it is pushed under the door most nights,' said the Patrician. 'Apparently no one is seen.'
From page 100:
A grubby cloth cap lay on the pavement. On the pavement beside the cap someone had written in damp chalk: Plese HelP This LiTTle doGGie.
Beside it sat a small dog.
It was not cut out by nature to be a friendly little waggy-tailed dog, but it was making the effort. Whenever someone walked by it sat up on its hind legs and whined pitifully.
Something landed in the cap. It was a washer.
The charitable pedestrian had gone only a few steps further along the road when he heard: 'And I hope your legs fall off, mister.'
And between Gaspode and Carrot on page 103:
'How do you manage to write, Gaspode?'
'I holds the chalk in me mouth. Easy.'
He's already a talking dog. You can't expect him to be able to spell too.