There are many inaccuracies regarding the layout of the White House. In Lincoln's day, the second floor Yellow Oval Room served as a library, not as his office. The cabinet room is incorrectly placed in the State Dining Room on the first floor. The current Lincoln Bedroom served as both Lincoln's office and cabinet room (hence the name) during his presidency.
One of the scenes set in 1862 depicts the assassination attempt made on Lincoln's life (where his hat was shot off by an unknown gunman and Ward Hill Lamon later retrieved it). That event actually happened in 1864, when Lincoln was running for reelection.
In one scene, Lincoln states he will be sixty-one years-old at the time his second term ends (on March 4, 1869). He was born on February 12, 1809, that would've made him sixty years-old at the time.