In the last scene just after Rex is shot and is lying on the floor of the mausoleum, the size, color, and location of the blood stains on his shirt change.
Nobody would be allowed to bring personal cell phones into a secure area at the CIA. Personal items such as Charlotte's purse would probably be banned as well.
During the scenes with the Blessing, a reflection of the green screen is clearly visible in Jack's knife a few times and once in one of his coat buttons.
The Spanish-speaking liaison, Sandra, is introduced as Sandra Lopez but credited as Sandra Morales.
The precise antipode of Buenos Aires lies in the Yellow Sea, more than 200 miles north of Shanghai. Charlotte Wills' attempt to explain this discrepancy - that the Earth is not a perfect sphere - would affect the elevation above sea level at the antipodal point, not its location as described by latitude and longitude.
When explaining the Blessing's effect to Jilly, The Mother states that "in 1998, the average life expectancy from birth on this planet was 66 years, five months, and 33 days." No month is 33 days long; this should either be "six months and two days" (assuming a standard month of 31 days) or "six months and three days" (assuming the standard is 30 days).
In the situation room, the boss says it is 11:09 AM in DC and 12:09 PM in Buenos Aires. Buenos Aires is UTC -3 and DC is UTC -5, only two hours in the time difference, not 13.