From a plot perspective, Elaida was fine, showing just how much of the Tower's incompetence was theirs alone, and couldn't (all) be laid at the feet of the BA.
She's a professional protege, she lies constantly, she never earned anything she got, and she's annoying as hell.
As for the idiot hat, I meant her constant bitching about Rand. She knows for a fact he's the Dragon Reborn, yet all she does is bitch about him.