Factual error: When the men are checking the store room for Rose and Jack, the men are using huge battery powered bright white flash lights that look like they're from Jurassic Park. Back then they would have produced yellow light. The light used in the movie was a Short-Arc Xenon bulb, you can tell this by both the very high color temperature of the light and the center of the light has a "hole" in it where the actual tube is blocking the beam. Such technology was not around at that time.
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.
Continuity mistake: When Rose is trying to rescue Jack she spies a fire axe. Smashing all the glass out from the holder she grabs the axe and turns round. The next camera shot shows Rose standing in front of the case with almost all of its glass intact.
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 reversed.
Continuity mistake: In the scene where Rose breaks Jack's handcuffs, you can visibly see the stunt person not wearing suspenders as Jack does. This is an inter cut shot between the raising of the ax and the striking of the cuffs. Leonardo's stunt double is noticeable in other shots throughout the film.
Continuity mistake: Look closely at the location of Rose's beauty-mark the first time you see her at the dock. It is on the opposite side of her face during the rest of the movie.
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.
Continuity mistake: When Jack and Rose finally come aboard the top of the ship after she rescues him they ask the Colonel if there are any boats left and he says "up that way" The woman on the left, who looks kind of pathetic, is then later seen on the life boat with Molly Brown. (They show her face right after Molly says the line "its your men out there") The life boat with Molly Brown in it was sent out before the scene with the Colonel, meaning that she must have gone on the life boat, swam back onto the ship and then back onto the lifeboat.
Factual error: During the drawing scene, 'Jack' is using modern square sided, pressed charcoal with numbers embossed in the side of it. In 1912, Jack would have been using vine charcoal which was round and made of 'charcoalized' willow twigs.
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.