Who was trying to gain power, and did anyone try to position themselves to be king or leader post-war at any point? What were their aspirations and what do we know about their intentions?
Many of the rivalries that mark the politics of the post-Constitutional era (like Hamilton vs. Adams vs. Jefferson and Madison) had not yet fully developed during the Revolution. However for much of the Revolutionary War there were serious challenges to General Washington, especially after Washington was forced to retreat in haste from New York. After the battle of Saratoga there was a "cabal" of officers who wanted to replace Washington with Horatio Gates. Over time, the challengers to Washington were defeated in various battles and their luster dimmed.
Later, Washington himself was accused of being involved with conspiracy to establish an American Aristocracy due to his involvement in a private club that was exclusive to Revolutionary War vets and their descendants. Washington at first was active in this group, but then he took pains to distance himself from this group, albeit in a gentile manner, so as to not give the appearance of trying to establish an aristocracy.
From about the second Presidential term of Washington there was a concerted effort lead by Jefferson and Madison to accuse the Federalists, lead by Hamilton, of trying to implement a "Monarchy". I see this charge against Hamilton and Adams being taught to grade school children even today. I personally am challenged to be able to know what part of these charges were true, and what part were early political propaganda.