Racism is an obvious issue. Rowdy, Junior's friend was almost racist against his own kind as he was mad at Junior for being open to spending time with white people. The mascot at Junior's new high school was an Indian which certainly felt a little racist to him.
Education is inequitable. On the reservation, it feels like education only occur for the students who want it, and at that, not many do. Most Indians drop out anyways seems to be a common attitude.
Government assistance is a consistent issue that dominates the text as medical help, type of glasses, and the welfare benefits or lack thereof are regularly referred to in Junior's narration.
Alcoholism is a consistent controversial issue on the reservations. In this story in particular, Junior's dad's friend Eugene is considered a regular drunk driver who Junior actually rides with during the novel at one point to get to school.
Violence is a system of managing behavior on the reservation. Parents express violence on children, and children establish pecking order among each other in this book.
These are the major controversial issues you will find in The Absolutely True Diary of a Part-time Indian.