During Sam and Olivia's discussion at the pump, Olivia's arms change between being crossed behind her back, in front of her chest and akimbo, depending on the camera perspective. At the same time, Sam is standing mostly behind the pump, but in one shot is leaning with his arm on top of the lever.
When Sam tells Isaac that Lincoln will be emancipating the slaves, Isaac replies, "That's fine if you live in the north." In actuality, the Emancipation Proclamation only freed those slaves that were in secessionist states. Northern slaves were not freed.
Olivia tells Sam the Confederates will hang him if he is lucky. This is untrue as the policy regarding captured officers was to generally exchange them for Confederate prisoners or parole them back to the Union (they could not fight unless given notice of an exchange) and would remain the policy until 1864.
When running down Isaac King's descendants, Al names Martin Luther King Jr.'s grandfather as Emmanuel King. In reality, MLK's paternal grandfather - and father of Martin Luther King Sr. (born Michael King) - was James Albert King (1864 - 1933). There are no surviving records of James Albert's parents.
Olivia owns a player piano, which wasn't invented until 1863 and not generally available until 1876.
Captain John Beckett's orders, dated September 2, 1862, were issued in the name of the commander of the Union Army General George B. McClellan. However, McClellan was relieved of his position on March 11, 1862 and succeeded by General Henry Halleck.
Al says that if Sam does not ensure that his great-grandfather John Beckett and his great-grandmother Olivia Barrett Covington fall in love, his parents will never be born. However, it would only be his father who would never be born.
Lt. Montgomery tells Sam that a particular handgun "hasn't worked since Bull Run". Montgomery, as a Confederate, would have known the battle as "Manassas".