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.
Factual error: Rose mentions Austrian psychoanalyst Sigmund Freud's ideas on the male preoccupation with size to Bruce. However this is 1912, and Freud did not publish the work relating to this until 1920 in "Beyond The Pleasure Principle." Also, up until 1919, Freud relied solely on data from females.
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.
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.
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: 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: The hymn that they sing at the church service about "those in peril on the sea" has four verses. "Peril on the sea" was written in 1860 but the verses that have "protect them by Thy guarding hand" and "O Spirit whom the Father sent" were not written until 1937, and thus could not have been sung at the service.