Continuity mistake: When Jack and Rose are on the way to the end of the ship to try and stay on as long as possible, you can see them jump down from a railing, but if you watch when Rose jumps down, a woman also jumps down next to her and falls over, yet in the following shot she has vanished, then in the background she can be seen jumping down again. (02:28:55)
Factual error: Rose takes the elevator down to rescue Jack. When the operator goes back up, the elevator moves when the gates are still open. In reality, the gates had to be closed before the elevator car could move. (01:54:00)
Factual error: The radio system in use at that time was based on spark transmission and we should never have heard a nice clean transmission of Morse code SOS or CQD beeps. (01:45:25)
Continuity mistake: In the scene you see Rose going down stairs, before she goes into the water she rests an axe on the door frame which turns to the side, yet in the following shot it's not turned to its side. (02:00:00)
Continuity mistake: When Tommy Ryan, one of Jack's ship friends, is trying to get to the top deck, but is stopped by metal guard rails, at the beginning of the scene he has his right hand on the rail, then in the next shot he has his left hand on the rail. (02:04:05)
Factual error: Regarding the church service on the Titanic, it was non-sectarian, however it was based on the Anglican Church in England (or Episcopal in America). The fact is that Captains did conduct the service, were open to anyone; thus Jack could not have been kept out. (01:12:05)
Suggested correction: On the real Titanic, 1st, 2nd, and 3rd classes were strictly segregated, not to mention the social attitudes of the era. Hence, no steerage passenger (e.g. Jack Dawson) would have been allowed onto First-class spaces. Furthermore, in real life, there was no single church service open to all on that day - Second class had their own service in their dining room (i.e., separate from First class).
Then, how did Jack get to go to dinner with the first-class passengers?
He was invited for saving Rose's life. (I haven't seen the scene in years, but I think Rose invites him.) Molly Brown then gets him some clothes. (I believe she mentions that he is her son's size.) Otherwise, he would not have been allowed in 1st class.
Continuity mistake: In the water, Jack and Rose climb on a floating piece of wood when a man in the background blows a whistle. First this man has a strand of hair over the forehead, a frame later it's combed backwards, then half a second later the strand of hair reappears. (02:39:35)
Factual error: When the captain declares to Bruce Ismay that the last boilers have been lighted, it's only half true. Sunday morning, the last "regular" boilers were lighted to reach a total of 24 out of 29. The five boilers of the auxiliary boiler room number one are not in operation yet. The day after, weather permitting, it was planned to light them on for a few hours to see if the Titanic had something in the ball. (01:13:00)
Suggested correction: He doesn't say that to Ismay. Ismay says, "I see you haven't lit the last four boilers," and Smith replies, "I don't see the need. We are making excellent time."
Continuity mistake: When the musicians go out on deck to play as the ship is sinking all they have on is their uniforms. They are seen this way a few times, in the last shot of them they all have on overcoats. (02:06:30 - 02:22:30)
Continuity mistake: Captain Smith is drowning. In one shot, the window busts and water leaks into the room with the steering wheel. In the next shot, the window is fully intact and breaks again. (02:22:50)
Continuity mistake: After Rose sees the Titanic, Cal replies "it's 100 feet longer than the Mauretania", with nobody behind him. Right then the angle changes and his chauffeur appears. (00:21:20)
Suggested correction: Lovejoy is seen further back. When Cal says its 100ft longer, he turns to help Ruth out of the car and Lovejoy is still further back. However due to the new angle, he appears closer.
Deliberate mistake: When the lifeboat crew are searching the water for survivors, they are using lanterns. It has been admitted by James Cameron himself that the real Titanic crew didn't have lanterns in the lifeboats, but this was the only way to light the shot. (02:45:55)
Continuity mistake: When Jack and Rose are dancing on the 3rd class level, Rose takes her shoes off and looks down at her feet, in the following shot she is looking at Jack, and the shot after she looks at Jack again. (01:05:30)
Continuity mistake: When the captain looks at the bridge sinking, the water level is by the middle of the helm wheel. In the next shot, from the other entrance, the level is lower than that, and in the next it's again by the middle of the wheel, which is also turned to a different position. (02:24:00)
Continuity mistake: When Jack and Rose are on the way up to the end of the ship, they go past a priest with lots of people praying, some are holding his hands, yet in the following shot, the people are not holding his hands, and are a bit further away from him than in the previous shot. (02:31:20)
Continuity mistake: During the break-up of the ship, David Warner's character, Lovejoy, is right where the gash starts. Right after we see the interior break-up shot, we see the hull breaking, and on the top, where Lovejoy should be, he is nowhere to be seen. (02:35:00)
Continuity mistake: When the diamond is found in Jack's pocket the way Rose's hair is messed up is different in every single shot. (01:41:45)
Continuity mistake: When Jack is dining in first class with Cal Rose and the others, when the men get up to leave, and in one shot you see Cal walk past Jack, and in the following shot he is walking past again. (01:02:15)
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 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)