When one considers that the man was elected unanimously to a job he didn't really want, then managed to keep the fledgling country together through the early, tenuous years after the Revolution, many would probably agree that he was a success. The first government of the United States was basically no government; wary of central governments that might become too strong, the colonies-turned-nation created a loose confederation of states under the Articles of Confederation, which basically established--pretty much nothing. The central government under the Articles could request most anything from the states--money, soldiers, cooperation--but enforce absolutely nothing. Once it was determined that under the Articles, there would likely soon be no nation, Washington presided over the Constitutional Convention, accepted the Presidency, oversaw the creation of a strong government, kept the nation out of wars for which it certainly was not prepared to participate in, established traditions like cabinet advisors, and because of the great respect with which he was viewed by Americans, most everything he put his stamp was approved. Known as the Father of the Nation, many historians believe that there was really no one else who could have done what Washington did because he was held in such universal and high regard.
Whether it was a success or failure is pretty debatable, and it is a tricky question here is a list of some questionable success and failures below.
1) Washington's nationalization of the states' debts, one way of consolidating and legitimizing the central government (under the new Constitution)
2) Washington's putting down the Whiskey Rebellion, a direct attack upon consolidating and legitimizing the central government
3) Washington voluntarily surrendered his office at the end of two terms...a VERY novel concept in late 18th Century political thinking...and allowed John Adams to be elected.
1) The XYZ Affair---Francophiles in the American government (read Thomas Jefferson) almost let the French undermine the new USA
2) The Alien and Sedition Acts---almost created a dictatorship
You can read this for some great info about George Washington and his life: http://www.enotes.com/topic/George_Washington