During the jousting scene, Elizabeth has shields display behind her with red next to black on them. Under the laws of heraldry, patches of red and black cannot touch other than at corners.
The depiction of the execution of Earl of Essex is incorrect. In the film, he is beheaded with a single stroke of the axe. In actuality, it took three blows to remove his head.
While Essex did persecute Dr. Lopez, leading to the latter's execution in 1594, in this version of the story, the Lopez investigation occurs before Elizabeth discovers Essex has impregnated Frances Walsingham, whereas Essex and Frances had been married in 1590.
Elizabeth and the Earl Of Essex play a game of cards. The playing cards are rectangular, but have rounded corners, a feature not introduced until the 19th century as a means to counter normal wear of use.
In an era long before plastic false teeth, Elizabeth is recorded as having one tooth left in her head before she reached the age of 20, yet Helen Mirren clearly has a flashing, gleaming smile.
Dudley was actually a few months older than Elizabeth and both would have been in their late 20's at the time of their romance, yet Helen Mirren at the age of about 60 is clearly extremely senior to Dudley.