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.
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).