Two possible negative consequences of rapid growth of GDP are rising inequality and the breakdown of traditional societal ways.
When GDP rises rapidly, there are typically winners and losers. We can see this today in China where there are billionaires at the same time that there are millions of very poor people living in poor conditions. As a country gets rich quickly, this sort of inequality tends to rise.
In addition, a rapid rise in GDP can break down traditional society. Again, we can see this happening to some degree in China. One thing that typically happens is that people move much more than they previously did. Mostly, there is movement from the rural areas to the cities. This breaks down the social ties that bound people together. It harms the society of the rural areas and it also makes social control harder in the city because there are so many people in new situations with no traditions to influence them to behave properly.
In these ways, rapid economic development brings problems as well as benefits.