Einstein said he "would still be a patent clerk in Vienna". That incorrect, Einstein was working for Federal Office for Intellectual Property in Bern, Switzerland between 1902 until 1909, not in Vienna, Austria.
In 1942 Rip Hunter disguises himself by wearing a British Royal Navy Admiral's uniform (note the insignia on his cap, and the rank insignia on his sleeve), but he only wears ribbons awarded by the United States to US military personnel, and no British military awards of any kind. In some cases the ribbons are not even appropriate for the time period. As a master of time, and by extension history, Rip Hunter should know better.
When trying to find the Legends who have been thrown out into time, Martin Stein and Jefferson Jackson are said to be in 'Tintangel, England'. This is a typographical error. The correct name is 'Tintagel' which is tied to the King Arthur myths, and is a village one can still visit where the ruins of the castle still sit. It is also known as Trevenna, and in the time that Martin and Jax would have been occupying Tintagel, it was known as Tintagol. It is the place where the Lady Igraine was hidden by her husband before Uther Pendragon (disguised by Merlin as her husband) seduced her. Their child was King Arthur.
At the beginning of this episode, while talking to Oliver Queen, Dr. Heywood mentions "Mesopotamian hieroglyphics" describing a ship "that disappears," and he shows a document which clearly contains Egyptian artwork. Cuneiform, the earliest known writing and appearing in Mesopotamia, consists of ideograms, not hieroglyphs. Not only did Dr. Heywood use the wrong terminology, he showed artwork from a completely different culture. Furthermore, unless what he showed to Oliver was a copy, the document would have been made of papyrus rather than what was clearly stained paper.