Factual error: When Gwen finds Toshiko's hidden message from 1941, she realizes that it was written in blood, and her flashlight reveals the bright red letters on the now-yellowed piece of paper. But after 60+ years, the iron in the blood would oxidize. The writing on the note should be rust-brown, not red.
Factual error: "Captain" Jack Harkness actually wears the rank insignia of a group captain, equivalent to an army colonel and never abbreviated to "captain". In fact, the RAF does not have a rank of captain (the equivalent rank is flight lieutenant). Neither does it have the position of "squadron captain", as he is described - a squadron commander in World War II usually held the rank of squadron leader (equivalent to an army major).