Also, she could have been searching for the seals Rand held, which she knows he kept hidden somewhere - retrieving even one of them would result in massive points from the Dark One. One of his palaces would be a safe bet as to a hiding place. Further, she might have wanted to Compel servants and such to become sleeper agents.

Graendal seems to have the best set of motives IMHO precisely because she is willing to get involved when necessary, especially if she thinks Rand is off distracted fighting another Forsaken. With Compulsion being one of her major skills, she can't help but do some tasks personally, which is why she had more agents than Lanfear did.