Factual error: Sir John Franklin, Francis Crozier and James Fitzjames all wear a crown over an anchor on their epaulettes, the rank badge for a captain with over three years in rank. This is correct for Franklin and Crozier, but Fitzjames only held the rank of commander, and should therefore only be wearing an anchor on his epaulettes.
Episode #5.7 - S5-E7
Other mistake: Two actors are standing on an ancient muddy track which shows the tyre prints of a modern vehicle, made probably by the 4WD camera car. (00:09:00 - 00:10:00)
Factual error: Johann Eck is dressed as a cardinal and Albrecht von Brandenburg addresses him as "Your Eminence" and kisses his ring. In reality, Eck was not a cardinal. Albrecht, however, was. It should be Eck showing deference to him, not vice versa. Albrecht was also only thirty, half the age of the actor playing him.
Episode #1.2 - S1-E2
Factual error: The settlers prepare to burn Verity at the stake as a witch. Witches were never burned in England or her colonies; they were hanged.
Factual error: Pierre Bezukhov's spectacles are of the type with nose pads, which were not invented until the late 1920's.
Continuity mistake: Tutankhamun and Suhad ride to the Mitanni city on a horse with no equipment at all, not even a saddle. Yet mysteriously when they need to stop for the night a large tent appears out of nowhere.
Continuity mistake: When the princess moves between rooms, the door in the first room is left well open, but when the shot changes to the second room, the first door is almost closed. (00:05:40)
Factual error: The Merchant Navy rank insignia is very poorly researched. Each officer seems to have a different style of insignia, despite working for the same company and they incorrectly wear rank insignia on the shoulders of their blue uniforms as well as the cuffs. The main character, Junior Third Officer Mortimer, wears a bizarre mix of insignia, apparently consisting of a Royal Navy petty officer's sleeve badge, a Royal Navy chief petty officer's cuff buttons, and a rank badge of three inverted chevrons on his shoulder boards that doesn't seem to resemble anything from reality. In reality, he should simply wear a single cuff ring (or shoulder bar in white uniform).