Dwight Crouch, the conspirator who fought with Gault in the fire-damaged part of the ship while trying to set off a bomb, was not included in the Ostara festival's list of recent deceased.
Approximately 15 minutes in, we see Samantha Kruger steal Carillo's multi-colored (i.e. multi-zone) key-card and replace it with her blue one, but moments later when Harris arrives, Carillo turns and a multi-colored security card is clearly still attached to his trousers. Kruger then leaves and uses a multi-colored key-card to access the cell where Stokes is being held. Further, when the security guard who challenges Kruger and Stokes in the garden scans the card she gives him, Carillo's face appears on his scanner.
In the series it is stated that the CO2 scrubbers use lithium dioxide to convert CO2 into water and oxygen. This is impossible, as lithium dioxide and CO2 do not contain any hydrogen atoms, which are necessary to produce water. Lithium hydroxide does in fact react with CO2, but does not produce oxygen. Lithium peroxide has the added benefit of also producing oxygen, but is almost never used.
When speaking about the film that was revealed at the ceremony, the Captain mentions he needs to find out who "uploaded" it.
This term would not have existed in the crews' vocabulary as they haven't had Earth contact since the 1960's.
Sound cannot travel in a vacuum. However, this is not truly a goof as there isn't really any vacuum.
Given the security in the bunker housing the Ascension, it is surprising there was no security lock on the doors marked "Restricted Access Zone" that Stokes went through to the outside of the Ascension.
Given how long it takes to make a baby, especially if pregnancy does not happen quickly, it is surprising the ship's passengers developed the strategy of announcing birth permissions once a year rather than shortly after each death.
Gault says that the carbon dioxide scrubbers contain lithium dioxide. In reality, carbon dioxide scrubbers contain lithium hydroxide.