Factual error: After the Fort Sumter battle, Mary Todd sees the newspaper on Lincoln's desk which states "20,000 soldiers dead", and what appears to be an April 1861 date (which makes sense since that's when the Battle of Fort Sumter took place.) However, there were zero causalities at that battle. And the first major battle, First Battle of Bull Run in late 1861, didn't even see 1,000 causalities.
Continuity mistake: In the final fight scene atop the train, Lincoln's African American colleague Will is attacked by the head vampire and is knocked backward over the side of the boxcar. He is seen with his feet nearly over the edge and Abe is seen 7-10' away, lying on the forward end of the car, facing him. In the next shot, Will continues his backward fall and Abe's arm appears over the edge of the roof, grabbing Will's leg. There's no way Abe could have risen from his position atop the car and covered the considerable distance in time to reach down and save Will.