Vetinari would probably:
1. Either get it shut down as a threat to A-M; OR
2. Organise it better.
For a start:
a. No uncertainty. Either dragons exist or not.
b. A definite end to the squabbling and infighting.
The rest is up to Vetinari. If he wanted to run Wyrmberg as a classic evil tyrant -- dragon rotas!
On Tuesdays, you, you and you fly down to terrorise these villages. On Wednesdays, you, you and you do.
OR, if he wanted to run it for the good of everything -- no dragon flying unless necessary!
And dragons can now only be used to start bonfires!
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Carrot would definitely try to arrest
everybody, while Vimes would be aghast.
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Moist von Lipwig would boss people around and run the whole thing more efficiently, but with lots of charisma (as he usually does).
But then, giving Moist that much power is a frightening thought.
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Nobby and Colon would flee ... and maybe run into some knights on a holy quest. =P
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Rincewind would roll his eyes wearily and say "What,
again?" while Twoflower takes pictures busily in the background.
... and so on ...