Episode #1.1 - S1-E1
Factual error: The American flag shown waving outside the White House is the current present-day flag with 50 stars. From 1896 to 1908, (the time period that this show is set in) the US flag only had 45 stars as Oklahoma, New Mexico, Nebraska, Alaska and Hawaii were not recognised as states in that time period. The flag did not have 50 stars until 1960. (00:04:30)
Black Blood - S1-E1
Other mistake: All the Greek name variants are used over the Latin ones - including even "Odysseus" over the more familiar "Ulysses" (who is the same person). However when the story of Actaeon comes up, it's suddenly the goddess "Diana" that he saw. But all the gods have their Greek names, so that should be "Artemis." (As indeed is used in episode 2). (00:39:35)