Particularly in the early books, there's a lot of mistrust on his part towards all Aes Sedai, especially her.

 

I can't really think of anything particularly devious that she has done to him.  Is it just the AS reputation?

Yes, for the most part it is, along with the fact that he knows she hides things/manipulates people, thats why things change in tSR and FoH (i am not sure if you have read them yet, so i will not spoil it) not sure if anyone has a different opinion, but that seems the general answer to your question

Plus, you have Ba'alzamon in the background inserting those threads of doubt into Rand's head. No matter how many times Rand tries to deny him in dialogue, it's obviously getting to him.

I don't know how far you've read, and I don't want to spoil things for you.  In the beginning, Rand doesn't trust her because it comes out pretty convincingly that she (and other Aes Sedai) just want to manipulate him.  And yes, their reputation is less than stellar.  Think about how the Two Rivers folks reacted in TEotW after they found out she was Aes Sedai - and they're all (generally) good people.  Aes Sedai reputation is not something that "good, honest, hard-working Two Rivers folk" find positive (for the most part).