Factual error: Trust called Proxima B an "eyeball" planet, meaning according to him a planet that does not spin on its own axis and always has one side facing the sun. That is incorrect. If only one side faces the sun it means the rotation on its axis and its revolution around the sun are the same.Otherwise, the planet would seasonally have all of its surface facing the sun once every solar year.
Revealing mistake: Hannah sits in a conference room and pulls a landline phone towards her to dial her friend, asking about the will Owen left. The phone however isn't in any way connected, hence no call could have taken place.
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.
Other mistake: Juliette and two cohorts need to go from Level 22 down to Level 125. Using the normal circular stairs, it would take several hours if not days to get there. They enter a garbage chute and climb down using a vertical ladder on the side - a very clumsy and slow descent. Yet, they make it in what appears to be a very short time.
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.