Among other problems, we can mention the following as the most serious ones:
It was hard for colonies to organize themselves and form a strong Government, given the fact they had never ruled themselves and had no experience in this area. Without a government, newly independent countries didn't have an army, so they were easy targets for coups, rebellions and even attacks from neighboring countries.
In addition to that, their economy was highly dependent of the former parent country, which made these countries struggle at first to figure out their trades, leading to economic crisis.