Abigail "Nabby" Adams' marriage to William Smith is shown while John Adams was serving as vice president. However, Adams and Smith actually married in June 1786, three years before John Adams took office as the 1st Vice President of the United States in April 1789.
At Washington's inauguration, the film shows one man both holding the Bible and administering the oath. In reality, Samuel Allyne Otis held the Bible and Chancellor Livingstone of New York administered the oath.
Alexander Hamilton wore a brown wig. He never wore a wig, though he sometimes powder his long strawberry blonde hair in a few occassions.
Alexander Hamilton was wearing a brown wig, when in fact, he didn't. According to historical accounts He had long light red hair that later turned blonde with gray highlights that he sometimes powdered as he grew older.