Robert Dudley recites Sir Philip Sidney's sonnet "My true love hath my heart" to Elizabeth in a boat. This sonnet was not written until at least 1580, about 20 years after the time the movie is set, and wasn't published until 1593.
Elizabeth is shown washing her face with water. In 16th-century England, water was considered dangerously unhealthy and almost never used for washing the body. Elizabeth would have "bathed" by rubbing her face with a dry cloth.
In the film, Bishop Stephen Gardiner stands as a key figure in the pro-Catholic faction during Elizabeth's reign. In fact, he died in 1555 before Elizabeth ever ascended to the throne. The role Gardiner plays in religious politics here is likely a stand-in for the historical Bishop Edmund Bonner, the Catholic clergyman most at odds with Elizabeth's Protestant reforms, who died as her prisoner in the Tower of London in 1569.
As Walsingham is speaking with Mary of Guise, she is holding a table knife up to her lips, and is playing with it by rotating the handle. The camera then switches to a shot from behind her head and the knife is oriented the other direction. Then, as they continue speaking, the camera shot returns to the original angle and the knife handle is reoriented back to the original hand.
At the beginning of the film when Elizabeth is being arrested, she is addressed as "Princess Elizabeth". She was stripped of the title 'Princess' when Anne Boleyn was executed and called 'lady'. Mary Tudor made certain that distinction was maintained during her reign as she followed Catholic Law and considered Elizabeth a bastard.
While it's true that Henri, Duke of Anjou (later King Henri III) was generally obsessed with clothing and did on occasion dress as a woman, he never actually traveled to England to court the Queen. That honour fell instead to his younger brother François, who became Duke of Anjou in 1576, and was the only one of Elizabeth's many suitors to court her in person.
The beginning of the film shows Robert Dudley with Elizabeth while she was arrested. Historically, Robert Dudley, his four surviving brothers (including Guildford), and his sister-in-law (Lady Jane Grey) were all in the Tower of London indefinitely. In fact, Wyatt's rebellion threatened all of their lives and brought about the executions of Jane and Guilford, while Robert and his remaining three brothers would stay in the tower until being released later that year.
Mary of Guise rides at the front of her men across a bloody battlefield. Back then, even reigning women did not ride at the front of their troops, and rarely rode horses with both legs over the animal; they sat on the side. It is actually said that Mary of Guise refused to ride in front of her troops.
Robert Dudley, the Earl of Leicester never betrayed Elizabeth and in fact helped to uncover the plots against her. He supported the execution of Mary Queen of Scots who was the chief threat to Elizabeth's throne. He was in fact one of her most devoted counselors until her death.
The first shot of Walsingham in the film (from behind the head), is actually used twice. Just before the next shot (of his face), a sharp slit of silver can be seen heading toward Walsingham's head from the right side of the screen. However, Walsingham's servant then crosses the room, and gets a knife out of its case. When the next shot of the back of Walsingham's head is seen, this slit is the knife now being held to his throat by the servant.
The goof items below may give away important plot points.
When Daniel Craig returns to England bearing letters from Rome, he accuses Norfolk's man, Thomas Elliot, of betrayal, then grabs him and leads him in front of Norfolk off to the side (closer to the shore). As he beats Elliot to death with a rock, Norfolk watches from the side. When the priest is finished, and Elliot lies dead in the water, he is shown coming down from a greater height, several yards away, and behind Norfolk, rather than a few feet off to the side.