What is Odo's dog hiding and how do you find out what's up with it?

Welcome to the age of information.

http://witcher.wikia.com/wiki/Odo_%28NPC%29

That doesn't tell me anything I didn't already know.

We don't know anything certain; it was never explained, and there is nothing more that can be learned about it in the game or in writings about the game. What we do know:

(spoilers if you haven't played further)

Odo murdered his brother.
Echinopsae grow where heinous acts have been committed.
The dog is guarding a place where Geralt just cut down an echinops.

Put these together, and they suggest, but do not prove, that this is the scene of the murder, and the dog has sussed this out after the manner of dogs.