The ship's version of the Pledge of Allegiance maintains a reference to God, yet no religion is shown among the characters, such as during Lorelai's funeral in the previous episode presided over by the Captain and his wife but no pastoral figures. One can argue both ways whether the experiment's designers would want or not want religion on the ship, yet the real constraint would be finding so many original mission volunteers without religion in the middle of the 20th century. Regardless, passengers would find the reference to God in the pledge odd if they believed in no such figure or had never heard of Him.
When the video of Lorelei's psychology exam is replayed, the answers that she gives are out of order from the first episode, and they also have slightly more detail, particularly about her father.
The vaccination dispenser requires a fingerprint, yet after Ophelia is given Christa's vaccine, another is dispensed without anyone's fingerprint.
When a woman exits the library onto a promenade during a transition shot about half-way through the episode, she closes the door behind her to a sound effect of a door closing and latching solidly. However, it can be seen from the crack of light around the edge of the door that it begins to fall open again after releases it. The prop door clearly has neither jam nor latch.
At 40:23, when Samantha Krueger clicks on the bio website for Eve Marceau, the text on the top half of the page is duplicated / repeated on the bottom half.
The reasons Harris gives for the Ascension passengers needing inoculations due to weakened immune systems is not valid, and it is difficult to believe a ship's doctor falling for this. It is true that an isolated population would be at risk of diseases like measles, due to lack of exposure, none of these pathogens could appear on the ship. When government workers enter the ship surreptitiously, they wear biohazard gear. Even an annual flu shot probably wouldn't be necessary. Of course, the current doctor would have been born on the ship and her medical education could have been tampered with to get her to believe the shots were necessary, but this sort of compromise would need to be carefully done in order to not cause broader problems with her knowledge.
The government agency controlling the Ascension ship has a broad network of surveillance cameras installed in the ship, and access to all the ship's systems to monitor them and even interfere. It's difficult to believe the hardware and wires for all this were never discovered by the ship's crew as they maintained their own systems--especially in the early years when technology would have been larger and clunkier.
The ship's reproduction system doesn't fully make sense. Matching couples through genetics could have some benefit, like preserving dominant or recessive traits, but since all original passengers were likely vetted for genetic strength, allowing people to pair organically would probably be fine. Controlling pairings might serve an experimental purpose or be intended to quash interpersonal problems, yet controlling sex and love is destined to cause more problems than it solves. Societies with marriage matching typically repress cultural notions of romantic love, yet those on Ascension are allowed access to Earth books and movies that would showcase young people falling in love and choosing to marry. Further, Harris tells the investigator Samantha that gay persons were left off because it wouldn't be fitting for anyone to intentionally avoid procreation, yet members of further generations could still be gay, and it's hard to believe they would be considered "superfluous" as Harris says given that they would also have a job on the ship. Besides this wouldn't really matter because it's been stated that a child can only be born when someone else dies. If couples can only reproduce at the replacement rate, there need not be an emphasis on forcing everyone to pair and reproduce. Those who wish to can maintain the numbers. And even though ship society would not have developed as Earth's did, forced reproduction is always a hard pill for women to swallow and would supremely undercut the Eden-like community shown on the ship. Further, it might even be the case that gay persons would be the least likely to fight back against marriage and reproduction, given the time period the ship's culture is stuck in--plenty of gay persons on earth entered into heterosexual marriages in order to hide their truth and avoid persecution.