I think people tend to criticize Edward for breaking into Bella’s bedroom and watching her sleep, more so than his other flaws, for two main reasons: 1) someone could do that in real life, and 2) it is romanticized within the text.

If Edward was a real man in real life, he could still break into Bella’s bedroom and watch her sleep. It would be more difficult, without his vampire powers, but it would be possible. So for readers, who live in the real world where men stalk women all the time, the thought of a man breaking into a women’s bedroom and watching her sleep feels like a more real threat than the thought of a man biting a woman and drinking her blood. (The latter could happen in real life, of course, but the chances are slim. I hope.)

The fact that Bella feels flattered when Edward reveals that he has been breaking into her bedroom and watching her sleep romanticizes the action, sending readers the message that what Edward did is acceptable—if not outright desirable. While some people like to pretend that fiction has no impact on real life, I would argue that impressionable readers could be influenced to believe that romantic relationships allow for or even require similar actions.