Revealing mistake: When Bolivar's assistant comes running out of the theater where she found him, there are New York cabs as well as Toronto cabs in the background. The passing ambulances are marked as from Toronto, not New York.
Continuity mistake: Goodweather and Setrakian find the body of Ansel's wife hanging in the stairwell of their home. When Goodweather removes the suicide note from her hand, a rosary is dangling loosely from her wrist. When the shot cuts to a viewpoint from behind her, the rosary is now entwined around her fingers. Then it changes back to hanging from her wrist again.
Continuity mistake: Fet is in the sewer looking for rats and encounters a group of infected. He is holding a handkerchief to his face with his left hand to mask the smell. He has his flashlight in his right hand, and pulls out an iron bar with his left. As the camera angle changes, his left hand is again covering his mouth with the handkerchief (no iron bar), then the angle changes again, and he's holding the iron bar again. (00:35:05)
Continuity mistake: Setrakian was born in 1921 and taken to Treblinka when he is 18-years old, that should be in 1939. The episode timeline states that he's taken to Treblinka's in 1944, which would make him 24/25 years old in this scene. (00:08:00 - 00:09:00)