La Rochelle - S1-E1
Continuity mistake: S1E1 La Rochelle. Kate is the new First Officer of the cruise ship, later she introduces herself as First Mate - a much lower rank.
Two by Two - S1-E6
Continuity mistake: When Alicia presents the slingshot trajectory, Eva says the solar sails will provide "more than enough" power to reach the planet with the U238. Shortly after the sails are deployed, the edge of one of them is damaged, causing the ship to lose enough power to start dropping back to the star. But you can see that about 1/10 of one of the six sails is damaged, or 1.7% of the entire sail array. How is "more than enough" reduced to "not enough" when they lose such a small part of the sails? (00:19:57 - 00:23:33)
Continuity mistake: When talking on the roof at the start, the guy in green has his hands in his apron pockets when being told the security cameras are off. Cut to a wider shot and his arms are folded instead.
Continuity mistake: Hannah enters the bar wearing a University of Texas hooded sweatshirt with its unmistakable school color when she asks Charley to take her to see her father. When they arrive at her father's house, she is wearing a plain dark sweatshirt.