Trivia: The reception room's double doors leading into the first class dining saloon only have bronze grilles in the movie. In 1912, there was actually a pane of glass in each door with the grilles behind them on the dining room side. On the collector's DVD commentary, James Cameron mentions they didn't discover this until a later Titanic expedition in 2001 - that's why this is trivia, rather than a mistake.
Trivia: When Titanic was re-released in 3D in theaters in April 2012 in conjunction with the centennial anniversary of the sinking, NBC News did a story on Nightly News. One of the things they mentioned is that an astrophysicist, Neil Degrasse Tyson, noticed in the original 1997 release that when Leonardo DiCaprio is lying on a bench looking at the night sky, the constellations are not correct based on the time of year and the location on earth they are being viewed from. Director James Cameron became aware of this error, and corrected the constellations in the night sky for the re-release in 2012.
Trivia: On set, Cameron was a furious perfectionist, often angering the crew with his attention to detail and furious nature. Eventually, one crew member got back at him by pouring a large amount of drugs into the food served to the rest of the cast and crew. 160 people ended up hospitalized due to the effects of the drug (although Cameron was not among them), and the poisoner was never caught.
Trivia: During the "Let's stretch her legs" scene, the engine room returns the command confirmation to the captain's deck of "All ahead full." The lead in the engine room yells out "All ahead full," and someone off camera repeats the line. The voice repeating the line is James Cameron himself.
Trivia: The shot of the lifeboats sailing towards the Carpathia was the only one in the film that was actually taken at sea.
Trivia: The scene at the end when everyone is running and the priest is saying "As I walk through the valley of death" to which an annoyed Jack responds "Could you walk a little faster" was taken from 1969's Paint Your Wagon where Lee Marvin and the preacher have the exact same exchange when fleeing the cave collapse.
Trivia: The seaman who is on the boat that returns and eventually saves Rose is Ioan Gruffudd in a very early role, portrayer of Mr. Fantastic in the Fantastic Four movies, the short-lived show Forever, and the Hornblower series. He's also shown after the seaman says "Get back, I say, or I'll shoot you all like dogs!"
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.