Continuity mistake: When Jack is showing Rose how to spit and is interrupted by the arrival of her mother, the glob of spit on his face moves from the side to the middle. (00:35:45)
Continuity mistake: When Rose is running to get to the stern to throw herself off she starts by running on the first class A-Deck promenade. Then when the whole stern of the Titanic is shown sailing, Rose runs out from the 2nd class B-Deck promenade, a deck down. The only way that these two promenades were connected was by two ladders, which Rose passes when she keeps running. It makes no sense to go down the ladders, go forward, turn around and head back to the aft part of the ship. (00:35:55)
Factual error: Early in the film Jack smokes hand-rolled cigarettes. When he is smoking on the stern deck before Rose is thinking about jumping, he is smoking a mass-produced filter cigarette. Filters in cigarettes didn't exist in 1912. (00:36:05)
Continuity mistake: When Rose approaches the stern railing to climb over it casts a very clear moonlight shadow on the deck which is not there in all other shots of this scene. (00:36:35)
Continuity mistake: In the scene where Rose is about to jump off of the ship, she gets to the end of the ship, and she climbs over the railing. At one point she's holding on to the black part of her dress, and it goes onto the long shot and she isn't, then close up she is again and so on and so on. (00:36:40)
Revealing mistake: In the suicide attempt scene, after Rose climbs over the railing, you can notice banding of the night sky a couple of times - that appears on both VCR and DVD. (00:37:15)
Continuity mistake: When Rose attempts suicide she is holding onto the railing while standing on the outside. In some shots the black lace from her dress is held under her left hand, in some it isn't. (00:37:40)
Continuity mistake: Early into Rose's suicide attempt scene Jack's hair tucks itself behind his ears while his hands are in his pockets. (00:37:55)
Continuity mistake: Rose is attempting to commit suicide and tells Jack to leave. When he says "No", his hair swaps from being all over his face to neatly combed, between shots. (00:38:15)
Revealing mistake: When Rose is about to commit suicide and Jack approaches, their skin turns pale and slightly blueish due to the green screen effect. This happens in all the wide angles from this scene where a big part of the sea and the horizon are visible. (00:38:30)
Factual error: The lake that Jack told Rose he went ice fishing on when she was threatening to jump is Lake Wissota, a man-made lake in Wisconsin near Chippewa Falls (where Jack grew up). The lake was only filled with water in 1918 when a power company built a dam on the Chippewa River, six years after the Titanic sank. (00:39:05)
Continuity mistake: When Jack is persuading Rose not to jump, Jack's shirt collar changes position several times, revealing his white t-shirt from a little to a lot. (00:39:05)
Other mistake: During Rose's attempted suicide as she's hanging off the back of the ship, a horizontal line of dark color is seen below her navel. It appears to be her personal undergarments: modern thong/hip-hugger underwear. (00:39:10)
Continuity mistake: About to jump off the boat, Rose says "You're crazy" and looks at the sea. A frame later, her head is turned towards Jack. (00:39:10)
Continuity mistake: When Jack is talking to Rose for the first time, his hair is constantly changing position. (00:39:30)
Continuity mistake: When Jack tries to talk Rose out of drowning herself, the camera cuts back and forth between their faces. There's a strong wind blowing through Rose's hair where Jack's hair is totally still in some shots. (00:39:40)
Revealing mistake: When Jack rescues Rose from her suicide attempt she slips. In the shot from behind when she is seen dangling precariously her (or the stuntwoman's) hair is longer and redder. Kate's stunt double is noticeable in other shots throughout the film. (00:40:55)
Continuity mistake: When Rose slips during her suicide attempt and Jack grabs her right hand there's a shot from behind where her left hand is holding on to the second railing bar from the bottom. When the camera angle changes she is holding on to the bottom bar, and in the next shot again to the second. It's unimaginable that she would change her grip that frequently in this situation. (00:40:55)
Continuity mistake: When Jack gets invited for dinner after Rose's rescue his hair changes between hanging down and tucked behind his ear alternatingly. There is another change after he puts Lovejoy's cigarette behind his ear. Similar alternating changes happen while he talks to Rose in the gym. (00:43:15 - 01:14:55)
Continuity mistake: When Cal gives Rose the diamond her front hair changes from shot to shot, most drastically when she says "good gracious." (00:44:30)
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.