Lincoln is shown playing "Dixie" on a Jew's harp. That portion of the film is ostensibly set in the year 1837, but most reliable sources indicate that "Dixie" wasn't written, publicly performed nor published before 1859. During the Civil War, Lincoln was known to be partial to the tune (it was almost as popular in the North in the 1860s as in the South), but it's unlikely he would have heard it in the 1830s.
In the opening scene, where Lincoln gives his campaign speech for election to the Illinois legislature, he states he adheres to the principles of the Whig Party. The scene takes place in 1832, but the Whig Party wasn't formed until 1836. (In 1832 Lincoln was a National Republican, the Whigs' predecessor party.)