There are many problems in Out of the Dust, but all of them seem to stem from two particularly big problems. The first is, of course, the dust storms. The dust storms have made farming for wheat nearly impossible and dashed any hope of most farmers making any kind of profit. This creates many problems for Billie Jo's family, which are only compounded by the failure of her father's bread shop, for which he had taken out a loan.
The second huge problematic incident is when Billie Jo accidentally throws flaming kerosene on her mother. This severely injures her mother and ultimately leads to her father drinking away her education money. Later, it also leads to Billie Jo's mother dying in childbirth along with the baby. It is because of this that the two remaining family members drift apart and Billie Jo runs away.
Thematically, a huge emphasis could be placed on survival and a sense of belonging. When Billie Jo runs away, her food is stolen by a homeless man and a photo of his family is left in its place. This reminds her that she belongs with her father and that they need to stick together to survive.