Continuity mistake: We see Mr Andrew walking through the 1st class cabins just after hitting the iceberg. He has 4 blueprint rolls under his arms. We then see him out on deck while discussing the situation with a few other men and the rolls have gone. As he gets to the office with Captain Smith he has the rolls again. (01:39:20)
Continuity mistake: When we see Jack and Fabrizo at the front of the ship, in one shot we see the wind blowing Jack's hair and jacket. In the next shot it's not. (00:29:50)
Continuity mistake: When Jack looks through the porthole (which is full submerged underwater) while cuffed, he looks over his left shoulder which is facing the hull of the ship. He then turns his head which cuts to him inside the room, his left shoulder is now facing away from the hull of the ship, towards the door. The shot of him looking through the porthole is possibly a reversed shot.
Chosen answer: During the several years it took to construct the ship probably, or in any of the supplies/food brought on board, or in the furniture brought on board. A single pregnant female rat can be responsible for thousands of rats in a very short space of time (the offspring are not too choosy about who they breed with).
Soylent Purple
A pregnant female rat could have made a home in a underneath a third class couch and had the other rats then all the females would have baby rats quickly.