Deliberate mistake: In the scene at the start of the movie with the "authentic" piece of film, you can see a girl with a hat waving to the people at the ground. When the ship is leaving port in the film, she and others are in the same positions, only in reverse, because the first "authentic" shot is the same shot, only mirrored. (00:00:40 - 00:25:30)
Deliberate mistake: In actuality, the Palm Court (the place where Rose, Cal, and Ruth have lunch with Thomas Andrews, Bruce Ismay, and Molly Brown) did not serve full meals. Only beverages and small snacks like tea sandwiches, pastries, and crumpets were served there. It is quite obvious that the group is supposed to be having lunch based on the items they order (sausage, lamb, salmon, etc). James Cameron probably set the lunch scene in this location rather than the First-Class Dining Saloon or the A La Carte Restaurant (the only locations where a First-Class passenger could order a full meal, besides their stateroom, of course) so that Jack and Rose would have a realistic chance of seeing each other for the first time, being as the Palm Court veranda overlooked the Poop Deck. (00:32:30)
Deliberate mistake: Even though the movie uses the correct number of rockets, the timing is awful. The last rocket was fired at 1:40 AM at the latest. In the movie, the last rocket is fired when the last boat to be lowered on the davits leaves (the one Rose gets, and jumps off of). This would make it 2:05 in James Cameron's Titanic time. It was probably changed to add more drama to that heart-throbbing scene... (02:18:30)
Deliberate mistake: When the lifeboat crew are searching the water for survivors, they are using lanterns. It has been admitted by James Cameron himself that the real Titanic crew didn't have lanterns in the lifeboats, but this was the only way to light the shot. (02:45:55)
Deliberate mistake: When Jack and Rose are adrift in the ocean, the stars behind them are not the right ones for that time and date. In fact, it's not any sky ever seen on Earth. The right half of the sky is a mirror image of the left half. The fimmakers deliberately positioned the stars to form the shape of the pendant 'Heart of the Ocean.' (02:46:00)
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.