In the opening scene, Corky and Mrs. Haverford share a yellow-labeled bottle of Veuve Cliquot champagne. The yellow label was not introduced until 1873.
The confederate spy states that he was held in a Union Army prison on Johnson's Island near Sandusky, and that people were rowed across the Ohio River the view the prisoners. However, while there was a military prison on Johnson's Island during the Civil War, there's no way people would have rowed across the Ohio River to go there, unless they then traveled across most of the state. The Ohio River runs across the southern border of the state of Ohio, while Johnson's Island is in Sandusky Bay, on Lake Erie, at the north end of the state.