What are two significant challenges the people in Eastern Europe and the former Soviet Union faced immediately after the collapse of communism?

I would argue that the two most significant challenges
faced by the people of Eastern Europe were A) setting up a new governmental system and
B) setting up a new economic system.  Both of these had to be done essentially from
scratch after the fall of communism.  This is a problem that has not completely been
resolved in all of these countries.

After the fall of
communism, these countries had to figure out how to maintain order and keep a government
running without communism.  None of these countries had had any experience of
non-communist governments in many decades.  This continues to be a problem as some
countries still have dictators or strongmen like Vladimir Putin in power and have not
really managed to become democratic.

The countries also had
to try to form viable economies.  This was very difficult since they had little
experience with private ownership, competition, or any of the other aspects of modern
capitalism.  Again, this continues to be a problem as countries such as Russia have what
is called "crony capitalism."

Having to create governmental
and economic systems from scratch was a major problem for Eastern European countries
after communism ended.