There are a few historical inconsistencies which don't really detract from the story's enjoyability. The biggest one is King Richard's death, which is overly dramatized for theatrical effect. While it is true he was shot by an archer, it was in the arm, so it took him almost 2 weeks to die from gangrene.
Historical accounts tell us that King Richard returned to his bankrupted kingdom in disgrace, and wanted to raise money for another Crusade. He was in the middle of suppressing a revolt in Limousin (in Central France), and it's possible he was also seeking to procure a cache of Roman coins discovered by a local farmer (much like his little brother John would do in later years, Richard sought to extract whatever funding he could from the people). During a morning's survey of the battlefield, Richard caught an arrow in the arm from a crossbow-wielding boy.
Thus ended the reign of Coeur de Lion, a Norman King who couldn't speak a word of English and had no love for the people he ruled. History has rewritten the king into a great leader, but he was really a piggish monarch who died a failure. On top of that, researchers have speculated that he may have dabbled in homosexuality, and it's possible he even had an affair with his own sister. How scandalous! Richard the Lionheart, indeed!
I expect you can see why they couldn't show the "real" King Richard in the movie. However, they did show him to be more pig-headed and arrogant than in previous versions of Robin Hood, so that's a plus.
The only other inaccuracy I noticed lies in the use of written English words on the sword's hilt and on different landmarks. Back in 1199, everything would have been in Latin, but I suppose that wouldn't have had as big an impact on the viewers, since few people can read that script these days.
Neither of these trifles diminished the movie's effectiveness, and in retrospect they probably improved it. This is historical fantasy, after all, so trying to get too accurate would be foolhardy.
I give this latest incarnation of Robin Hood 4 out of 5 stars. I really hope they have a sequel in the works, because they did a good job of setting up a whole new series with this one.