Revealing mistake: When Stevens leaves the house about halfway through and sits on a bench there is a modern electrical outlet on the wall to his left.
Factual error: In one of the scenes in which took place in a white room, on the door behind the character's head is a modern day "door closer". Door closers were invented in 1880 by Lewis C Norton of the the LCN Company and the first one was installed at Boston Trinity Church in 1880, was some 15 years after this film took place.
Factual error: In the flag ceremony Lincoln raise a US Flag with 35 stars which was in use from 1863-1865. Later, Lincoln is riding through the aftermath of a battle scene and the soldier following is carrying a flag which matches the 1877 US flag with 38 stars.
Continuity mistake: When Lincoln is giving his soliloquy about abolishing slavery, if you look close, Secretary Seward"s elbows are on the table with his hands folded and his chin resting on them. Soon after, When Lincoln says "Blood's been spilt to afford us this moment!" you'll see that Secretary Seward pulls his elbows off the table and onto his lap. The next cut is Lincoln pointing to Seward and the rest of the bunch screaming "Now! Now! Now!" At this time, Seward's hands are back on the table in the exact position they were before.