Factual error: Eichhorst seems to be unsure what his SS rank is. He is addressed as Standartenführer (Colonel) but wears the epaulettes of an Obersturmbannführer (Lieutenant-Colonel) and the collar patch of a Sturmbannführer (Major). In addition, his other collar patch bears the standard SS lightning runes instead of the death's head of the Totenkopf concentration camp personnel.
Factual error: In the scene where the shadow of the eclipse is seen from space, the shadow forms an almost continent-wide and elongated "swat" of uniform darkness across the Earth, which is astronomically impossible. Real total solar eclipse shadows are circular, with only a small area in the middle being inside heavy shadow (the Umbra) at any one time, with a larger area of half-shadow (Penumbra) surrounding it. The area inside the eclipse shadow is also far smaller than the one seen in the episode. Also, in the same scene, New York is seen to be near the edge of the shadow, meaning that the perfect solar corona that appears in a later scene should not be visible from there, since it's only visible near the shadow's center.
Continuity mistake: During the flashback scene, when the young Setrakian is attempting to hide his crushed fingers, both hands are wrapped in cloth strips. Eichorn unwraps Setrakian's left hand to inspect it, then sends Setrakian to the group that is to be immediately executed. Moments later, the wrap is still on, but when Setrakian is forced to kneel, his right hand is suddenly bare. There was no time to remove the other wrapping nor could Setrakian have done it himself, his fingers were too severely damaged.
Continuity mistake: When Eph and Nora become passionate while they are at Eph's former home, Eph is wearing a thick, outdoorsy-type jacket. Eph picks Nora up off the bed and carries her over to the bedroom wall, still wearing the jacket. The shot changes angle, and even though he never sets her down and she is tightly clinging to him with her arms and legs wrapped around his body, he instantaneously no longer has the jacket on and is wearing a sweater. He never had time to take the coat off and never set Nora down.
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.
Factual error: They're handling the box/coffin in the warehouse. Eph says it's 2.7m (9 ft) tall and from the looks it has about 1x1m base. So volume is around 2.7 cubic meters. The coffin is filled with soil which has density of ~1200 kg/m3. So in real life the coffin with its contents would weigh around 3200 kg or 3.2 metric tons, making it impossible to handle by hand. The wooden coffin would also break very easily if tried to lift with that amount of soil in it. The antique hinges, and that lone latch on the inside, are the obvious weak points of the construction and would break/give in on the real life. Also later on the episode when "the box" goes missing Eph is mentioning it weighs only 500 lbs (~225 kg).