One thing that kind of bothered me about this episode was how Tywin commanded Mace Tyrell to fetch him quill and paper. They mentioned multiple times how the Lannisters are in need of the Tyrells, so even when seeing Mace as an "oaf", I would think Tywin is smarten than showing such a lack of respect. Even Cersei didn't want to insult him in the books, if I remember correctly.