Be balanced. At that time, you had to choose sides. Either you were a Federalist - one who agreed with Alexander Hamilton and believed in a strong central government, or you were a Jeffersonian - one who agreed with Thomas Jefferson and believed in a smaller central government. Although he had his opinions, Washington did not choose sides and decided to have both Hamilton and Jefferson as part of his government. To be a good leader, you must understand the merits of both sides.
Foster relationships. I get by with a little help from my friends. The Beatles may have sung these words about 200 years later, but Washington probably said this as well when talking about France. Without the help of the French Navy, the British would have likely won the war. Great leaders know how their party affects the others, and such leaders constantly reach beyond their specific areas of influence.
Learn from your defeats. General Washington only won three of his nine battles. He was persistent and continued battling and learned from his mistakes, which prepared him for the third and most important victory, the Battle of Yorktown. It was the last major battle before the end of the war, thus illustrating that defeat is merely a set-up for the more important victories in the future.
Be humble. You are not greater than the cause that you represent. Washington was elected for two straight terms and would have easily won his third, but he felt that too much power would have been rested on him. He walked away from power for the good of the country. If you want to be a true leader, know the difference between benefiting yourself versus benefiting the greater good.