On the jousting scene where William loses his helmet, he has a monstrous bruise under his right eye (in the late afternoon). That night at the banquet, there is no trace of the bruise. So far as I know, even a black eye doesn't completely heal that quickly.
Several of the named knights were, in fact, real, though many of them are from different time periods. Ulrich von Lichtenstein was a knight and author who was said to have invented the concept of chivalry and courtly love. Piers Courtenay was a descendant of Edward I, born in the 15th Century. Sir Thomas Colville, Edward III's disguise, was a knight from the 13th Century. Lord Roger Mortimer was the lover of King Edward II's wife - Isabella of France - and was hanged, drawn, and quartered by the Black Prince's father, King Edward III.