Katniss choosing to hunt in the woods almost everyday shows Katniss's determination to protect and feed her family, as well as her bravery, as she is breaking the law and going into quite a dangerous area filled with animals that could kill or injure her.
During the reaping, Katniss volunteering as tribute when her sisters name was called shows that she is selfless and is willing to do anything for her family.
In this scene Katniss and Peeta are talking on the roof of the tribute center and in it Katniss is debating with herself weather or not to trust Peeta, this shows Katniss's mistrust for people.
One of Katniss's weaker qualities is her care for her family. Her care for her family may turn against her. When a hero cares about someone as much as Katniss cares about her sister, it is almost always used against them.
When Katniss is talking about her shooting she underestimates herself. She is modest, and that can lead to her not being confident with her skill.