In the opening sequence Dr. Mathewson is seen with blood on her chest after being dragged on the floor by Rowan, then we see her with no blood on her chest just before she uses the bone saw on herself.
Lommie says that no one has ever gone as far out into interstellar space as their journey will take them, to which Mel replies "Except Eagle 16". Later in episode 6 another character says that Eagle 16 was reported to the public as having been destroyed in an ice field near Europa and only high ranking Eris officials knew otherwise.
When Melantha and Lommie are beginning their first make-out session, Melantha's bare shoulder switches between left and right depending on the shot angle.
When Lommie goes to visit Jhirl in her cabin, Jhirl's top is hanging off her right shoulder. It switches sides multiple times.
When one of the Nightflyer's engines fails, a crewmember unbuckles from his seat and floats to a panel as if in zero-g. At this point the ship is still under thrust, which means he should not be able to float in this way.
When one of the Nightflyer's engines fails, a crew member unbuckles from his seat and floats to a panel as if in zero-g. At this point the ship is still under tons of thrust, which means he should be feeling g-forces pushing him back into his seat.
When the Nightflyer first begins to accelerate, a crew member floats as if in zero-g. This defies the laws of physics, since there would be g-forces from the acceleration pushing him towards the back of the ship.