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: When Jack Barts is lying on the ground, right before Abe kills him, his right hand is empty. When he is lying in the casket and Adam opens his hand, there is Abe's pocket watch.
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.
Factual error: When Abraham and Speed are hiding in the belltower, Speed bumps into the bell's pulley and it tolls loudly. The nudge wasn't hard enough for the bell's clapper (pendulum) to hit the side of the bell.
Continuity mistake: While Henry is talking to Abe in the bar after some time of training, we can see that his face has healed. However, in the next scene where he shows Abe the vampire targets, his face is as beat up as before.