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: 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.
Gavin JacksonTrivia: 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 PurpleA 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.