China's biggest weakness is its cultural narrow-mindedness.
Chinese people often think everybody else in the world holds the same values and traditions as do people in China.
For example, Chinese people often think everybody in the world honors their parents and ancestors the same way Chinese people do (xiao shun).
This extends to all areas of interpersonal customs, really. Chinese people simply cannot imagine other cultures and societies where interpersonal relationships are different.
Another example, Chinese people think that, because wealth is status in China, wealth must be status everywhere else in the world too. But in fact, status can include things other than wealth in other countries.
In contrast, people educated in the West can at least IMAGINE other societies with different cultural beliefs and values, even though they might disagree with those values or find them distasteful. Chinese people can't even imagine this, and instead thinks everybody in the world holds Chinese cultural values.
The only way China can resolve this weakness is by increasing social science education -- especially psychology, sociology and anthropology.