Friedrich List's first book was released in 1835 when he returned to Germany, not in the USA as shown in the movie.
Friedrich List did not lose his position as consul, as mentioned in the movie. In 1834 he was even appointed by Andrew Jackson as consul in the Kingdom of Saxony, which helped him gaining the citizenship of Saxony.
The opening credits mention that after Friedrich List founded the German Customs Union he flee to the USA. While the first Customs Agreements were created in 1820 the German Customs Union was founded in 1833. List's life in the USA was however from 1825 till 1833.
At the time of List's imprisonment in Hohenasperg in 1821 List's family is portrayed with only one daughter. In real life they had two kids, Emilie, born in 1818, and Oskar, born in 1820. Also a third child Elise, who was born in 1822 was on the way.
The Map of the German states that are shown by List to the parliament is incorrect. At the time the scene is set (end 1810s, beginning of 1820) Bavaria and Austria were part of the German Confederation and customs.
The famous folk tune "I've Been Working On The Railroad" is played on several occasions in the movie. The song was first released in the 1890s, while the scenes are set in the 1820s. Additionally the tune is inspired by the overture of "Poet and Peasant" by Franz von Suppé, which was released in 1846.
In the redaction scene between List and Ritter the tune "John Brown's Body" can be heard playing. This tune the way it was played in the movie was first released in the 1850s, while the scene takes place in the 1820s.