I used to teach American Lit, and it seemed as if the script used a lot of the words of the principals, but did it accurately reflect their meanings?
Not terribly.
The character of John Adams is actually an amalgamation of John and Samuel Adams. Thomas Jefferson is only a shadow of the actual man, and the compromise over the issue of slavery was not nearly so central as the play makes it. The issues they discuss are largely those of concern to people at the time, but they're expressed in odd ways (again, the issue of slavery taking a more important role than it really had in the debate).
As an alternative, I would recommend the second episode of John Adams. It's still far from perfect, but certainly closer than 1776.