In 1748, John Newton's fiance is seen singing in the church choir. (20 minutes into the movie). The hymn heard, "It Is Well With My Soul", was not published until 1876--by Horatio Spafford and Philip Bliss--fully128 years AFTER this story takes place.
On the slave ship, dead slaves are shown wrapped in canvas tied with rope, before they're thrown overboard. Slavers would never have wasted canvas and rope in that way. Dead slaves were simply tossed overboard unceremoniously.
Soon after the group of four runaway slaves met up with the Quaker conductor, the map used to indicate the circuitous Underground Railroad route shows both Virginia and West Virginia along with Maryland and Delaware. In fact, West Virginia did not become a state until 1863, seven years after the setting of the film in 1856.
In the English Church, a man is seen wearing a hat. Never done in Christian churches: Women at the time were to have their head covered, while men removed their hats.
John Newton was an English slaver, and became a Christian after a shipwreck off the coast of Ireland. It was not on its way to America.
The escape to Canada was through Western New York. The only falls there that border Canada are Niagra Falls and they and that river cannot be crossed on foot.
In the scene backstage at the theater, everyone is singing while the piano is being played. The style of the music is from the 1930's; nothing of the sort was around in 1862.
After hiring him, Jefferson Monroe (David Rasche) tosses Plimpton (William Sadler) a Silver Eagle dollar which prominently displays a walking Lady Liberty with "LIBERTY" spread across the top. This particular coin was only recently minted in the 1980's, having been based off of the "Walking Liberty" half dollar minted between 1916 and 1947 which was designed by Adolph Weinman who wasn't even born until 1870. It would have been far more accurate to have a "Sitting Liberty" dollar coin that did exist in that era (minted 1840-1873), but did not have the symbolic "LIBERTY" embossed on it.
The locomotive and the boxcar are too modern (ca. 19320 - 30) for that period.