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 Jack gets 2 pints in the 3rd class party, he hands one to Rose. Who then drinks it. When Rose is given the pint, there is a decent head on it. Camera cuts to her drinking and there is no head at all. (01:06:20)
Continuity mistake: In the scene where Jack and Rose are on the third class level partying with the other people in third class. When Jack hands Rose a glass of beer, how she holds the glass differs between shots. (01:06:20)
Continuity mistake: As Rose shows the men she can rise up on her toes, from the front she has a cigarette in the first three fingers of her right hand. In the next shot her right hand is seen under her left arm and she has no cigarette. When she falls back into Jack's arms the cigarette is back in her right hand. (01:06:50)
Continuity mistake: When Rose and Cal are on the private promenade drinking coffee, Cal puts his coffee cup on his saucer plate twice. (01:08:00)
Factual error: When Cal overturns Rose's table, there is a serving cart with modern-day casters. (01:08:10)
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. (01:10:40)
Factual error: When Jack goes up to first class on a Sunday morning, the group is singing the Navy Hymn "Eternal Father." What is impossible is that they are singing the verse written for Aviators. The verse starts "O Spirit, whom the Father sent." They are singing the whole stanza continuing with "to spread abroad the firmament; O Wind of heaven, by thy might; Save all who dare the eagle's flight, And keep them by thy watchful care." The last line "From every peril in the air" can only be heard in the background as Jack is arriving on the scene. The Wright Brothers flew about 8 years before, and this verse was not added until the late 1930s. (01:11:00)
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.
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 Rose is talking to Mr Andrews about the lifeboats, her bag changes hands instantly. (01:13:10)
Continuity mistake: When Jack is sneaking over the rail to the first class deck, a boy is preparing to spin his toy top. As Jack leaps the rail and begins walking, the boy throws the top and you see it start to spin. The camera angle then changes to show Jack walking, toward the coat he is about to 'borrow', and in the background you can see the boy again drawing back to toss his toy top. Since you have to meticulously wind the string around the top of the toy, it would be impossible for him to be making a separate toss. It's obviously the same toss filmed from two separate angles. (01:13:40)
Factual error: In the famous "I'm flying" Scene, the sunset is to the couple's left. But at that time (April 14) the ship was definitely steaming due West, and the sunset should therefore have been directly in front (or even a bit front-right). (01:17:00)
Continuity mistake: The length of Rose's fingernails changes noticeably throughout the film. In some scenes, her nails are very short (during the "flying" scene), and in other scenes her nails are a lot longer (when she takes the comb out of her hair right before Jack sketches her). (01:18:40 - 01:21:20)
Continuity mistake: When Jack holds the diamond his nails are clean and perfect. When he starts to draw they are ugly cut and dirty, revealing they're somebody else's hands (later known to be director James Cameron's). (01:21:00 - 01:23:30)
Visible crew/equipment: When we see Jack moving the sofa for Rose to lie on, look in the window behind him to the right. You can see the cameraman's shadow moving with the camera. (01:21:25)
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)
Continuity mistake: When Jack is about to start drawing Rose, the shot cuts back and forth from a close-up to a wider shot. In the wide shots Jack is holding his charcoal pencil, in the close-ups he is not holding it. (01:23:10)
Continuity mistake: Just as Jack begins to draw naked Rose, he draws a dark line down the center of his paper. In the next shot of the page the line is suddenly much fainter (over to the right) and he is now drawing her face. (01:23:15)
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. (01:23:30)
