One quite important group of social problems that China is facing are a cluster of demographic transitions, brought about to some degree by rapid industrialization and economic growth and to some degree by its one child policy. The first of these demographic changes is a rapidly aging workforce, in which the numbers of people working is declining with respect to the number of pensioners that need to be supported. This is further complicated by the breakdown, partially caused by smaller families, of the traditional family-based programs of care for the aging. This demographic change requires China to ramp up both availability of medical care and facilities for senior citizens, but moving from the traditional family-centered system to a state-centered one requires a shift in social attitudes.
The second social problem facing China is gender imbalance. The combination of the one-child policy and a strong preference for sons has led to significant gender imbalances, and a rise in numbers of guanggun (bare branches), or unmarried men, which may lead to increases in crime or other forms of social unrest. This is exacerbated by their strongly patriarchal society in which marriage for women, even those with careers, results in a disproportionate share of domestic labor, making many well educated women reluctant to marry. Solutions can either involve banning sex-selective abortion, relaxing the one child policy, or increasing support mechanisms for married working women, all of which would meet strong political resistance from some quarters.
The third major social problem you should address is the "hukou" or residency system that ties social services to villages of origin even for people who have moved permanently to cities. On the one hand, this created a social underclass and is a system unpopular with villagers, but many city residents do not want to change the system. Both preserving and changing the current system are politically unpopular with some groups, and yet some change is necessary.