Benjamin Franklin's 20-year-old son William was his assistant in the kite experiment, but is nowhere to be seen in the extensive sequence recreating the famous event.
Benjamin Franklin was not the founder of the Pennsylvania Gazette, which predated Poor Richard's Almanack and was not the same publication under another name. He bought the Gazette in 1729 and published it until 1766 when it was bought by other publishers. Poor Richard's Almanack, which ran from 1732 to 1758, was a publication unrelated to the Gazette, and ran concurrently with it.
When Amos reads Ben's rough draft of "Poor Richard's Almanac", it indicates a sunset happening at 7:43. However, Amos states in the narration prior to this scene that this is supposed to take place in the winter time, and during that time of the year in this part of the world, sunset usually occurs about three hours before that time.
While Amos is writing his contract for him and Ben to go over, he writes the word "binding" in a completely different text format. This is to emphasize the importance of this clause.
Governor William Keith was the benefactor who took over the teenage Benjamin Franklin's newspaper apprenticeship in 1723 (sending him from Pennsylvania to London), and then made Franklin the scapegoat for Keith's financial mistakes. The film has the two first meeting in 1745, when Franklin is already an established publisher.
Amos tells of the Mayflower sea voyage (1620) and then segues into the life of painter Hans Holbein (died 1543), but doesn't tell the viewer that these scenes are out of order.