Factual errors: The balloon would not be allowed to float untethered since there would be no way to steer the balloon back to the ship. It would be totally at the whim of prevailing winds. The fixed-location engine would be totally useless to steer the balloon since there would be no way to rotate it to the direction opposite of the direction they wished to travel.
Continuity: When Laura spots Peter through the telescope, Peter is looking off at an angle as if he is waving and smiling at a second ship that is present.