Plot hole: Episode 1: All passengers on cruise ships have a passenger card with their name and cabin number imprinted. They are not just identical key cards like in hotels.
Continuity mistake: Episode 15, "FaceOff": Sophia gives Elias one hour to get the buses or else she will destroy Washington. When this happens, the sun is high, and by the time the buses arrive it is already very dark outside. (00:03:05 - 00:34:15)