Factual error: On the way into the health spa, Wilberforce's friend says they should hurry or they'll be late. Wilberforce replies "the waters have been here for a million years - how could we be late?". In the late 1700s, no-one in Europe thought the world was that old.
Continuity mistake: When the Prime Minister is preparing to make his golf swing, his shawl is alternately bunched up and then spread out smoothly.
Audio problem: In the very final scene where the Scottish pipe band is playing the tune "Amazing Grace", it is apparent that the music is overdubbed and professional musicians were not used for the visuals. When the pipers are slow-marching, the marching is shoddy with different people stepping at different times ("experts" would be very precise). As the camera pulls back past the drummers, it is clear that some of them are beating their drums at a very different time to the sound track.
John Newton: Although my memory's fading, I remember two things. I'm a great sinner and Christ is a great Savior.