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.
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: 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.
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: 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.
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 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.
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 scene, when Cal calls back to Rose, Molly is still walking up to them.
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: In the early scene where Jack wins the tickets for the voyage, his hand-rolled cigarette is thin and almost done just before he shows his hand. About five seconds later, the cigarette is fatter and longer.