What problems or issues did George Washington face?

The major issue faced by George Washington was president
of the new United States was to get the country off on a start to democracy.  It would
have been very easy for the country to become something of a monarchy and there were
those (like Alexander Hamilton) who would have welcomed this.  By resisting this
temptation (to become king) Washington set the US on the path to becoming a true
democracy.

When Washington became president, there was
little precedent for a country that did not have a ruler.  In some way, Washington was
going to need to govern the country well yet, at the same time, keep from having the
political system revolve around the president as an individual.  This is a challenge
that many other new countries have been unable to solve.  Because Washington was able to
solve the problem, the US became a stable democracy instead of becoming a country ruled
by a series of strongmen or dictators.