Adams was wedged between two of the most dynamic, and intelligent men of the late 18th Century, Hamilton and Jefferson. He was a weak administrator, and completely outclassed by both of these men. He only managed a few real successes during his Presidency, most notably his policy regarding France, and the resolution of the Quasi-war. I like Adams however as there is no doubt that his moral character was of the highest caliber, and was a keen and just observer of human rights and justice. But he is somewhat reclusive in nature, which curtailed his ability to administer as he needed to during his Presidency. He frequetly retreated to his estate and left important issues on the table, undecided for long periods of time. The real Great man of this period was his predecessor, George Washington, who was able to keep both of these two dynamic personalities (Hamilton and Jefferson) largely in check, and use the best ideas of both, although Jefferson often felt he was being overlooked.
As for the series, Hamilton is not the arrogant, scheming elitist, and Jefferson is not the humble, good-natured gentleman that is presented. Both were hopelessly uncompromising, with Hamilton easily the most intelligent visionary, Jefferson, the most aristocratic and naive idealist, and Adams was the quiet spoken reclusive patriot. Still, I believe that Adams was the most faithfully done of the three, as his personality and nature was well captured by the actor, yet I will have to watch more of it to see how badly Hamilton was demonized.