Oh gosh...
It taught that Bella didn't mind Edward being around her while she slept.

Which is rather odd, wouldn't you agree? I don't care how incredibly attractive a guy is; I'm pretty sure that I would be a bit disturbed if I found that he was watching me sleep.

No, I don't think it's odd for a girlfriend to be okay with a boyfriend being around at night.

(Believe it or not, some couples even LIVE together, in the same house! Some even share a bed!)

No. In fact it kind of implied the opposite. The fact he left so quickly that Bella wasn't sure she'd imagined him shows he knew it was the wrong thing to do. The atmosphere in the whole scene was imo purposely a bit creepy. At this stage of the story we weren't supposed to know whether he was a good guy or a bad one, only that Bella was attracted to him.

@cassie-1-2-3: Yes, I am aware of that. However, I find it disturbing that someone would watch another person sleep without that person's permission. Just showing up and staring at a sleeping person, even one whom you know well, is somewhat creepy.

Okey dokey.

I think that Smeyer kind of puts it off as "romantic'. To me it's just creepy.

Unless the readers are vampires, then no, it didn't imply that they should creep into someone's room at night and stare at him/her sleep.

If it was Mike, for example, who watched Bella sleep and she thought it was romantic, it would be a different story. But it was a vampire. In a fantasy book.