aircraftfixerJuly 08, 2012Well.....
David; although in cahoots with Vickers, probably thought of her as a meddling bitch. Throughout the film, she was always lurking around and keeping an eye on David and everybody else. She was perhaps a thorn in the side of David's mission (working for Weyland). She didn't believe one thing about this mission.
Even though Weyland was very superficial in his co-operation with Shaw's faith, David could be said to have felt more strongly toward her- as she was looking for the same thing (however, different application) as his boss Weyland. 
He viewed her dreams.
He might have done this to interrogate her mind for clues to what was motivating her. Might have done this to spy for Weyland too.
But I don't think so.
As an android, he is without emotion. But chemical/physiological responses- Life in the form of a heartbeat, elaborate emotions and reflexes are something that a machine can see and perhaps appreciate in another "machine".
She is a version of what he was created to impersonate. She is the same species as his creator. 
Human.
Without emotion (namely Passion) he could in fact appreciate her specific individuality. Rather than Vickers, or the other shallow characters. I think Shaw has what it takes to "Turn him on"...