(at around 57 mins) When Themistokles returns from the ship of Artemisia telling the others that "The next time that we face her, she's going to bring all of hell with her." he looks to the side and in a close-up his contact lenses are clearly visible.
(at around 19 mins) Extra wearing what appears to be white tennis shoes as she prepares food(?) when Queen Gorgo and Themistocles first meet. She's an older lady with her skirt gathered in one hand at the back wall.
(at around 21 mins) Artemisia, sitting in her captain's seat, is eating an apple. When she first takes a bite, it is green. A closeup of her hand at a different camera angle appears and the apple is red. Switching back to the original camera angle--the apple is now green once more.
Admiral Artemisia's street-urchin back-story is completely fictional. She was born with a proverbial silver spoon in her mouth to the royal family of Halicarnassus in what is now Turkey, and inherited great wealth and power.
(at around 1h 30 mins) In one of the last lines in the movie Themistocles notes that "All of Greece has united against you, Delphi, Thebes, Olympia, Arcadia and Sparta". In fact most of Greece remained neutral and the powerful city state of Thebes was allied with the Persians. It is of course possible Themistocles was simply bluffing, but the tone and finality of the scene implies otherwise.
(at around 22 mins) It's not a mistake that the severed head blinks. Oxygen remains in the brain for several minutes after a head has been severed. There are reports of the heads of guillotined victims looking around and even attempting to scream. So, this is probably a recognition that in reality, the beheaded victim would have had a few minutes of awareness, including that he was being kissed by the woman who'd just beheaded him.
Darius I of Persia, father of Xerxes I died of health issues in October 486 BC, four years after the battle of Marathon in 490 BC. He was not killed by Themistocles shooting an arrow 1000ft onto a moving ship.