Final answer:
During Washington's presidency, the United States faced challenges such as foreign policy issues with territorial integrity threats from Native Americans, the British, and the Spanish, as well as domestic dilemmas involving economic policy and political division between Republicans and Federalists.
Step-by-step explanation:
George Washington's presidency was marked by multiple challenges, significant amongst them being foreign policy issues related to the settlement of the borderlands. Native American tribes, along with British and Spanish interests, threatened the United States' territorial integrity. Washington's administration worked to address these threats through military and diplomatic means, aiming for a peaceful settlement in the west and unhindered navigation of the Mississippi River.
Domestically, Washington also faced the dilemma of economic development and crafting a foreign policy that balanced French and British interests. The philosophical and political divide between the pro-French Republicans and the pro-British Federalists, including other important domestic issues like the Whiskey Rebellion, underscored the partisan atmosphere, especially towards the end of his administration. These domestic challenges further complicated the governance of the new nation.