Progressivism: Satrapi is clearly concerned with Iran's inability to fully embrace modern (good, from her perspective) values such as equality, individual freedom, etc.
Traditionalism/Fundamentalism: The alternative to Satrapi's hopes for a more liberal Iran are deeply challenged by a fear-based religious fundamentalism. This is probably the most profound problem, in Satrapi's vision.
Authority: Satrapi's relationship with her parents is a good representation of her struggle to be critical of her country. This seems to be the only way to grow up, for her.