Trivia: Ben Affleck reportedly based his performance on real-life men who were convicted of murdering their wives, in order to lend to the "did he or didn't he?" mystery of the film. In particular, Affleck took inspiration from Scott Peterson, a man infamous for murdering his wife and unborn son in 2002, and was surrounded by a similar media circus to Affleck's Nick Dunne.
Trivia: Tyler Perry was reportedly not aware of director David Fincher's body of work, and was cast without knowing Fincher was directing. Perry has stated that he likely wouldn't have taken the role if he knew about the darker work Fincher is generally involved in, but stated that he was glad he did take the role in the end.
Trivia: Hollywood actress Reese Witherspoon was a fan of the novel and purchased the rights, intending to play the role of Amy herself. However, once David Fincher was attached as director, she opted to serve only as a producer, realizing she wasn't right for the role.
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