Continuity mistake: When Boxey plays with Muffit, a red chair on the right sits away from the wall and turned slightly. Boxey and Muffit leave the room as Serina and Apollo argue, and when Apollo walks toward the chair, it is not turned as much and is much closer to the wall.
Continuity mistake: While on patrol, Apollo enters a void in space, where no stars or other navigational fixes are visible. But in at least one shot, his ship is shown from the left side with stars in the background. It's the shot immediately after Adama says, "That's odd."