In episode 1 it is revealed that King Richard became King and ruled for 13 glorious years. (1485-1498). This incorrect, Richard ruled for 14 years, (Edmund spent a year in prison after being betrayed before taking the throne for himself).
Any inaccuracies regarding Richard III and his close family are preemptively "explained away" by the opening montage, which explains that Henry Tudor later rewrote history to suit his own agenda.
Prince Edmund claims the title of Duke of Edinburgh in 1485, but this title was not created until 1726, just 19 years after the final union of England and Scotland. This is one of many gags in the series, as explained on the DVD special features.