I think Anna...
...seems a little bit shallow and insensitive, completely unaware of William's feelings when he is obviously uncomfortable. She doesn't seem to behave like the humble person they are trying so hard to sell us. At that birthday scene, Anna doesn't hide her salary to a guy that doesn't recognize her, making him feel uncomfortable. Later she is unable to pretend to enjoy the meal, stating that she is vegetarian. She even has the nerve to talk about her very difficult life stating a series of facts in a very superficial manner.
In many different occasions Anna treats William very poorly, and she reacts very childishly at the restaurant scene. A more believable, intense and strong reaction would have shown more than merely confronting the guys and talking about their parts. Besides, guys like that would have probably answer back at her.
I think the story loses quite an opportunity to portray the struggle a famous actor goes through from a deeper point of view. The movie in my opinion doesn't show - it tells, and it tell too much. It doesn't allow the audience to analyze - it tells them how they should feel, what to think, when and how much we have to like Anna.
And the thing is that Anna is not a likable character. There absolutely no scene in which I empathize with her. She is a selfish person.
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I'm not bad, I was drawn that way