Mold on her feathers, maybe? Does she bathe or get misted often? If so, maybe she doesn't dry completely under her feathers and harmless mold can grow. I wish I had my microscope handy (in storage somewhere). I would have you send me a feather and look at it for mold. Maybe your vet can look at the feather under a low powered scope.
When one of those dirty feathers falls out I would try washing it with a little soap and water and see if it's on the surface or inside like @saxguy64 suggests.
Since most cockatoos are white their feathers show every bit of dirt, mold (if that's possible) and any imperfections perhaps from when developing as bloodfeathers. I'm thinking that colored or dark feathers probably have imperfections too that we can't easily see.
