Bruce Ismay: But this ship can't sink!
Thomas Andrews: She's made of iron, I assure you, she can. And she will. It is a mathematical certanty.
At the party in steerage, a foreign-speaking man is speaking with Rose and she says "I'm sorry, I can't understand you." The man is Swedish, probably a friend of Sven's, and he's saying to her "Talar fröken svenska?" In English that translates to "Does the miss/lady speak Swedish?" which she obviously doesn't. See more...
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Visible crew/equipment: When the ship is sinking, there is a shot of Victor Garber leaning against the wall in deep contemplation. The camera angle is very tilted and a few things slide off the shelf in front of him. Look carefully on the DVD and you'll see a wire coming out under his arm behind him pulling the china cup off the shelf.
Continuity: When Jack and Rose are talking on the deck. Rose is explaining to Jack why she considered jumping. She stated that she felt that she was screaming at the top of her lungs and no one was listening. He looks at her ring and states that she'd sink straight to the bottom...yadda, yadda, yadda. If you watch that scene, pay attention to Rose's hair. One second, her hair in perfectly curled with bangs, then it is behind her ears. It alternates back and forth: bangs, no bangs, bangs, no bangs until she grabs his portfolio and they sit down on the chairs to look at his drawings.
Continuity: 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.
Continuity: Just as Titanic breaks apart, the compass platform (seen in front of the third funnel when the lights were still on) suddenly disappears. The water isn't even high enough to have reached its aft-most legs. The white projection on the deck that held the chandelier in the lounge is also gone, and the ventilator that sits on it is flush with the deck.
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.
Revealing: When Rose is running in the hallways trying to find help for Jack when he is hand-cuffed, she finds a man and asks him to help her free Jack. She gets frustrated with him and says "listen" then hits him. In shots before (you can put it in slow motion to see it) you can look at the man's hand and it already has blood on it before he touches his face.