Let's examine this by considering some of the characteristics of a dystopian society:
Conformity is expected and individuality is punished. We see this characteristic throughout Panem. Most notably, each District is required to send one boy and one girl tribute to the Hunger Games each year, and all but one of the group will die. Citizens are always expected to adhere completely to the rules of the Capitol; traitors have their tongues cut out and become an Avox. Of course, Katniss herself becomes a representation of individuality when she refuses to play by the rules of the Hunger Games, threatening to kill herself in a double suicide rather than kill Peeta. Her lack of conformity makes her an enemy of the Capitol and sets up the next book in the trilogy.
The society is presented as perfect but has many, deep flaws. The citizens of the Capitol most readily reflect this "perfect" life. Citizens there dye their hair and skin in bizarre colors as a matter of art and fashion. They enjoy lavish parties and wear grand clothes that look more like costumes than actual clothing. Disturbingly, they also enjoy the great "sport" of the Hunger Games, gathering with excitement each year to watch children kill each other. This reflects the depth of the flaws in this society. The citizens have no remorse or compassion for the death of innocent children and instead seem so far removed from the truth of death that they consider it more fiction than reality. They are detached and aloof, and their temporary sympathies for the death of a favorite child have no meaningful impact on them.
There is a feeling of being under constant surveillance. Even before Katniss arrives at the Hunger Games and truly is monitored every second of every day, she knows that her actions in District 12 are monitored. Thus, she is very discreet about her hunting activities, which she must do to feed her family. Katniss also mentions the Peacekeepers, who are tasked with public whippings for those caught being disloyal to the Capitol and sometimes are more violent, possessing automatic weapons to effectively end any attempts at breaking the rules.
Katniss's actions bring to light the flaws in their dystopian world in a way that no one has been brave enough to do before, and she provides a platform that demands change for citizens all over Panem.