Also, the center of mass of the ship is irrelevant. Even if the ship were rotating as it fell, the conservation of angular momentum would keep the contents rotating with it. Only if there were angular acceleration on the vessel (as in the bridge crew trying to upright the ship as it fell) and there was a simultaneous gravity failure would anybody be tossed about.
Wrong. If the ship is rotating, the people inside are going to be slung to the extreme edges if there's nothing like artificial gravity holding them in place. If there were no air or bulkheads in the ship, sure, they'd just float in place while the ship rotates around them. But the instant the person hits a bulkhead or is acted on by the fluid (air) around them, some of the ship's angular momentum is going to be translated to them by way of a force. If nothing else acts on them, they'll travel in a straight line, eventually hitting the outer bulkhead of the ship they're in. However, if you have a continuous force from the ship by way of a rotating bulkhead or the contained air, that person will be pushed into a rotation around the ship, which imparts a centrifugal force which forces them to the outer bulkhead again.
Note that I'm just pointing this out in general, I'm not necessarily agreeing with the theory that this is what happened in the movie.