The car scene where Bella figures out Edward ...she is soooo close to knowing then truth:
Isabella Swan: Did you follow me?
Edward Cullen: I... I feel very protective of you.
Isabella Swan: So you followed me.
Edward Cullen: I was trying to keep a distance unless you needed my help and then I heard what those low-lives were thinking.
Isabella Swan: Wait. You say you heard what they were thinking?
Isabella Swan: So what you... you read minds?
Edward Cullen: I can read every mind in this room apart from yours. There's... Money. Sex. Money. Sex. Cat... And then you, nothing. That's very frustrating.
Isabella Swan: Is there something wrong with me?
Edward Cullen: See... I tell you I can read minds and you think there's something wrong with you?