Adoption problems aren't formulaic like those in the physical sciences nor are they impossible to solve. Obstacles in adoption can begin before a home study and arise years post-placement. It's the way of life and adoption is not immune to it.
Problems that can arise before placement are more common for nontraditional adopters. If you're gay, disabled, a single parent, or older than the average adopter, you'll probably have trouble adopting an infant or working with certain domestic and international agencies.
Problems that may occur during an infant placement with a birth mother include her changing her mind or having to deal with a semi-open or open adoption where the future birth mother's parents are involved.
International adoptions are known for having a lot of delays due to paperwork. This means the child will need to remain in an orphanage or foster care while the adoptive parents stay in the child's country and wait for the adoption process to catch up with the placement.
Assuming an adopter has already passed a home study and been placed with a child, problems that may arise post-finalization could be related to the adoptee's mental or physical health. Sometimes an adoption can be disrupted by attachment issues, particularly if these children have moved around a lot in the foster care system. Support groups and counseling can help make handling these problems easier.