The biggest omission I've come across so far is the work John Adams did on the Constitution of Massachusetts. After a year and a half in France, Adams came home in 1779 and was almost immediately chosen as a delegate to the state constitutional convention. John Adams, Samuel Adams, and James Bowdoin were put on a committee to draft the constitution. Samuel and James selected John to work on it alone.
On October 30, 1779, after a month and a half, printed copies were ready for the convention to review. The constitution was inspired by existing state constitutions and Adams' previous work in his Thoughts on Government. Excerpts from the state constitution were later found in some form or another 10 years later in the United States Constitution.
All men are born free and equal, among which may be reckoned the right of enjoying and defending their lives and liberties; that of acquiring, possessing, and protecting property; in fine, that of seeking and obtaining their safety and happiness (Article I).Although there were some alterations, they were minor and Adams was still proud of his work. Afterwards, Adams would state to a friend:
The people have a right to keep and to bear arms for the common defence. And as, in time of peace, armies are dangerous to liberty, they ought not to be maintained without the consent of the legislature; and the military power shall always be held in an exact subordination to the civil authority, and be governed by it (Article XVII).
I take vast satisfaction in the approbation of the Massachusetts Constitutions. If the people are as wise and honest in the chose of their rulers, as they have been in framing a government, they will be happy, and I shall die content with the prospect for my children (McCullough, p. 224).The mini-series keeps Adams in France for an extended period of time neglecting to write his wife until he eventually asks her to join him. In reality, he made it home after a year and a half, wrote the constitution, saw it ratified, and he headed back to France with 2 of his sons (John Quincy and Charles).
As for the importance of the constitution, McCullough says it best:
As time would prove, he had written one of the great, enduring documents of the American Revolution. The constitution of the Commonwealth of Massachusetts is the oldest functioning written constitution in the world (McCullough, p. 225).
With a life as rich as John Adams lived, it is easy to leave out some aspects, but this is one I would have attempt to squeeze into the 7-part mini-series.
Full Text of Constitution of the Commonwealth of Massachusetts (1780)
McCullough, David. 2001. John Adams. New York: Simon and Schuster.