Revealing mistake: When Octavia storms into the lab where the Mountain Men have been holding the Ark's people, she has her sword in her right hand. As soon as Kane speaks she makes to sheath it, and we hear the sound we're used to expect to accompany that motion, but you can see she's just holding the unsheathed sword behind her. Then she proceeds to drop it, hiding part of the action from the camera with her body, and although you don't see her catch it again that is made evident from the way she eases the sword on the floor beside her right foot a moment later. Furthermore, in the next shot her sword is not in its sheath.
Continuity mistake: In the scene when Octavia and Maya enter the mess hall while trying to escape the guards chasing them, you can see Maya is walking in front of Octavia. In the shot immediately after, though, Octavia is the one in front and she is being stopped by a guard pointing a gun at her. In the following shot we are back to Maya walking in front still trying to cross the hall, just as she sees guards appear from around the corner; that is the point when the two turn around, and we are once again presented with the same shot of the guard intercepting Octavia, only from a different angle.