The most amazing thing about the success in the founding of this country is the fact that an unprofessional citizen militia repelled the most powerful military in the world.
The closest situation I can think of in modern times would be if Sarah Palin's husband's 'Secession' party faced and then repelled the American Military to go on to establish the Republic of Alaska.
The problems of a fuzzy chain of command and lack of basic resources such as blankets and adequate rations at certain points of the war were compounded by the extreme differences in the philosophical views of the various participants in the war over just what Liberty was.
Members of the 'gentleman class' such as George Washington wanted to create some sort of parliamentary system independent of Great Britain, but certainly not the radical Athenian Democracy patriots such as Thomas Paine wanted. Slaves took Liberty to mean their divine right to be free and fought both on the British/Loyalist and the rebel side. Merchants took liberty to mean an end to crushing tariffs and the ability to have commerce benefit them and their community.
There were of course advantages the American Militia had, a perceived moral superiority, familiarity with the terrain, a supportive citizenry (non loyalists at least) but the single greatest advantage it had was the Atlantic ocean. Throughout history, the protection of the supply line and ability to relieve troops has been the greatest decider of who is victorious in war. The difficulty of moving large amounts of troops and supplies over the Atlantic made it necessary for the British to try and have a quick and decisive victory. The longer the war drug on, the more it would be to the advantage of the American rebels.
George Washington was a successful military man, having served in the Virginia militia in the French and Indian Wars. He was a practical man just what the future nation needed.
Although there was a Continental Congress that gave George Washington vague command over a small federal Army, this was certainly not the professional standing Army we have now with paid soldiers.