Revealing mistake: When Rose lets go of Jack's hand and he sinks to the bottom, if you look closely enough, you can see Jack's eyes move under his lids, even though he is supposed to be dead already.
Factual error: When Jack is handcuffed to the pipe below decks, the elbow joint is a modern welded joint, not a bolted flange joint as in the rest of the ship. I'm sure this was done to allow Jack to move about with greater ease as the water level rose. (01:47:50)
Factual error: When Jack, and Rose were trying to escape the rising water they were trapped by a locked gate. Jack and the crowd pulled up a bolted down bench to use as a battering ram. When they pulled the bench loose they showed a close up of the wooden floor shattering. The wood was pressed fiber board which would never be used as ship decking, not to mention, pressed fiber board wasn't invented until decades later. (02:06:05)
Continuity mistake: After being shot at by Cal, Rose and Jack race down the hallways outrunning the rising water. Rose is wearing white sneakers, yet she is seen two minutes later wearing period shoes when Jack retrieves the gate key that the crewman dropped beneath the rising water. (02:17:05 - 02:18:50)
Revealing mistake: When Rose is running in the hallways trying to find help for Jack when he is hand-cuffed, she finds a man and asks him to help her free Jack. She gets frustrated with him and says "listen" then hits him. In shots before you can look at the man's hand and it already has blood on it before he touches his face. This was fixed in Blu-ray version. (01:59:05)
Continuity mistake: Just as Titanic breaks apart, the compass platform (seen in front of the third funnel when the lights were still on) suddenly disappears. The water isn't even high enough to have reached its aft-most legs. The white projection on the deck that held the chandelier in the lounge is also gone, and the ventilator that sits on it is flush with the deck. (02:40:30 - 02:41:40)
Revealing mistake: When the ship tilts to a vertical position, you see people falling and hitting objects on the deck. In a close up of that, you can see that a black and bronze-topped capstan has wrinkles in it and bends when someone hits it. Fixed in Blu-Ray version. (02:36:40)
Continuity mistake: When Jack and Fabrizio are at the bow, the anchor well below them is black. Along with that, the foremost railing is not connected with the rest. But when Rose and Jack are there the well is white and the railing connects. Plus during the "flying" sequence the gap between the vertical bits of the railing is different in different shots of the ship. (00:30:40 - 01:17:35)
Factual error: The car which brings Rose and Cal to the docks at Southampton has an RB registration plate. But RB wasn't introduced as a car registration index mark until 1929. (00:20:30)
Factual error: When Rose, Jack and his friends come up to the boat deck while the ship is sinking, they ascend using the second class staircase and its exit on the deck. When Jack lets go of the door it is able to hit the side of the deckhouse. On the actual Titanic there were walls on the bow side of each door, which supported an overhang above the entrance. This is not included in many scenes in the movie. (02:08:05)
Visible crew/equipment: When Jack and Rose are running away from Cal to the first class dining room, if you look at the glass you can see a black screen, a light, and a crewman. Fixed in the Blu-ray version. (02:20:32)
Continuity mistake: When the ship is about to leave the dock, there's a lot of people saying goodbye to the ones that are going to leave the city. In the following shots, you can see Jack and his friends playing cards inside the pub. If you look through the window you won't see anyone. In the next shot, when Jack leaves the pub, the crowd is there again. (00:23:15 - 00:25:05)
Continuity mistake: When Rose and Jack run through the dining room with Cal shooting them, notice that the floor is tilted to reflect the ship sinking. In the next scene when they run down the stairs, the floor is now perfectly level. There is no tilt to the floor. Notice how the water tumbles out of the door - it falls on a flat surface and disperses evenly with no angle to it. (02:16:05)
Continuity mistake: Right before dinner, Jack and Rose are talking to the Astors, and Molly comes up from behind them, asking Jack to escort her to dinner as well. In the next shot, when Cal calls back to Rose, Molly is still walking up to them. (00:58:15)
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)
Factual error: When Jack and Rose are being chased by the bodyguard, they run through the ship's boiler room, prior to winding up in the car. Titanic was fueled by coal, and the boiler workers were called the "black gang" due to what happened as a result of working there. Yet Rose was wearing a pale dress which stayed pristine after going through the area, as did her shoes. She should have picked up at least a little soot along the way, at least on her shoes and the hem of her dress. (01:28:00)
Visible crew/equipment: As Jack is getting ready to draw, when Rose comes out you can see a hand opening the door for her. (01:21:40)
Revealing mistake: Many scenes used computer graphics to show the length of the ship. Passengers were also added walking on deck. The shadows for the passengers don't always match. (00:30:25)
Revealing mistake: When Tommy, Jack and Rose are trapped down the staircase with a lot of other people, during the shot where Fabrizio is running towards Jack, look on the right portion of the screen. You can see a kid with a hat on, being carried around by his mother, who deliberately grins at the camera. (02:03:40)
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)
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.