Continuity mistake: Some scenes were shot after Rosamund Pike had gained some weight, following the plot of the book correctly. However, they were edited together very badly, so that the extra pounds (most visible on her face) come and go several times during the montage showing what she did during the first two days of her "kidnapping." Pasty face with puffy cheeks, and sleek face with taut skin over jutting cheekbones switch back and forth in what amounts to a matter of hours in the film's plot.
Continuity mistake: Fairly early in the movie, Margo comes to see Nick, who is upstairs in a bedroom. The press is outside clamoring, and Margo locks the deadbolt on the front door. After her talk with Nick, she's in a hurry, rushes downstairs and opens the door without unlocking the deadbolt, although they've added the sound of a deadbolt unlocking.
Continuity mistake: When Amy kills Desi by slaughtering him, the amount of blood on her left shoulder disappears and reappears, depending on the shot.
Answer: To my knowledge, the purpose of hitting herself was two-fold. First of all, a facial injury would support the idea that she was abused or in some sort of bad situation. And secondly, to help mildly alter her appearance, so she could blend in more. (Especially considering people were looking for her).
TedStixon