There are lot of human rights issues and injustices. Here are a few of them.
1. Mistreatment of women. They are dehumanized. Remember the scene when one of the soldiers was going to take advantage of the women, before the protagonist's father stepped in and defended her.
2. People's property were taken away by the local militia for their own gain with no punishment.
3. People were killed with little thought of life or death.
4. Religious oppression towards people who did not believe in what the local powers believed.
Injustice is a major theme in The Kite Runner, and the primary victim is Amir's childhood friend and servant, Hassan. When they are children, Amir witnesses (and sometimes participates in) the oppression of Hassan based on his class, ethnicity, and religion. Hassan's status as a Hazara (ethnicity) puts him at the bottom of the social ladder in Afghanistan. He is marginalized due to his "inferiority," at least according to the majority group, the Pashtun, which is the group to which Amir and his family belong. Ethnicity is tied to religion, as well, as many Hazaras also belong to the minority sect of Islam ans Shi'a Muslims. Hazaras cannot be educated, either, so there is really no possibility of social mobility. Thus, Hassan and his father Ali are poor servants who live in a small hut behind Amir and his father's mansion.
As a result of his ethnic, religious, and social class status, Hassan is regularly bullied and harassed, especially by Assef. Amir finds himself weak and unable to come to Hassan's defense. Amir feels his own sense of superiority over Hassan flare up when Assef bullies Hassan instead of defending his friend, to whom he was at one time as close as a brother. When Hassan is sexually assaulted by Assef, Amir is in shock and does not act to help Hassan. After the assault, motivated by his own shame and guilt, Amir frames Hassan for theft and, even though Amir's father forgives Hassan, Ali and Hassan cannot bear to stay, and Amir never sees Hassan again. The story of Hassan and Amir's childhood relationship is a very personal one, but it also gets at the inequalities and injustices inherent in the structure of Afghani society.
Later in the novel, when Amir tries to save and then adopt Hassan's son, Amir runs into more examples of injustice both in the government and embassies (in the adoption process) and in his experiences with the Taliban. The Taliban is seen executing an adulterous couple during halftime at a soccer game. While the Taliban deems their actions an injustice, the moral high ground taken by their leaders, like Assef, proves to be hypocritical. Amir discovers that Assef is abusing Sohrab, Hassan's son, and Amir fights Assef and with Sohrab's help is able to escape. The road to bring Sohrab home is filled with obstacles, partially because of his Hazara background and the Taliban's hold over the country. Even when they return home to California, Amir and Sohrab must suffer the prejudice of Amir's father-in-law, also a former Afghani citizen and member of the majority group.
Ultimately, Amir's journey to redemption shows that it is possible to fight injustice and oppression and in some way to right the wrongs of one's youth. However, the novel also emphasizes the brutal and oppressive conditions in Afghanistan and awakens in the reader a desire to see injustices righted.