In the movie, the seaman steering Molly Brown's boat says "There'll be one less in this boat if you don't shut that 'ole in your face." As in many items with the movie, the line is authentic. Except 1) it was not said to Molly Brown, 2) it was not said by that seaman, and 3) it was not said in that lifeboat. Check A Night to Remember for the actual circumstances. (In fact, Molly Brown not only wasn't subdued by the loud-mouthed seaman, she faced him down later.)
In 1898 (14 years prior to the Titanic tragedy), Morgan Robertson wrote a novel called "Futility." This fictitious novel was about the largest ship ever built hitting an iceberg in the Atlantic ocean on a cold April night. The fictional ship (named Titan) and the real ship Titanic were similar in design and their circumstances were remarkably alike. Both ships were labeled "unsinkable." This uncanny foresight by Morgan Robertson was mentioned at the beginning of Walter Lord's book "A Night to Remember" on which the 1958 British film was based. The comparisons and similarities are stunning, right down to the findings of an investigation after the sinking which blamed "excessive speed" for the tragedy.
Until Avatar surpassed it in 2010, this was the highest-grossing film (in North American and worldwide) of all time. It was also the first to gross over a then unheard-of $500 million (its total gross is $600 million) in North America alone, and the first to gross an amazing $1 billion worldwide.
When the Titanic splits and the rest of the ship begins to sink, next to Jack and Rose there is a man in white drinking whisky. This man actually existed. He was the chef who put on loads of layers of clothes and stole a bottle of whisky from the kitchen. He drank the whisky to keep warm, and he survived the ice.
Rose asks Mr. Andrews if he is going to make a run for the boats. The real Mr. Andrews was actually asked this question; it is rather clear what his answer was. Also, he is seen carrying a small notebook which he uses to note down reminders, tips, and pointers as to how to repair, replace, and improve certain areas of the ship. That notebook has survived.
Gloria Stuart (old Rose) and Kate Winslet (young Rose) were the first two actresses to be nominated for an Oscar for playing the same character in the same movie.
James Cameron actually drew the entire picture of Rose himself and it was sold at auction in 2011 for $16,000.
At the end when Rose is lying on the wooden door she is looking at the sky singing "come Josephine..." When you look hard you see that the stars in the sky are symmetrical. You can actually draw a line in it. [That is not exactly the case. If you look VERY carefully (this is much more effective on a big screen), you can see that the stars form the outline of the famous necklace, The Heart of the Ocean. I guess Cameron was a little bored that day.]
In one scene you can see Colonel Archibald Grace escorting two ladies to a lifeboat. Rose then asks if there are any lifeboats left and he replies, "This way, I'll show you." He did actually survive, a lot of people presumed he died. He wrote an autobiography stating that he climbed aboard the turned over lifeboat. You can actually see him in the film hanging onto the lifeboat wearing the top hat trying to cut the ropes.
It seems director James Cameron had some inspiration from an earlier Titanic movie. When Jack enters the grand staircase for the first time, "On The Beautiful Blue Danube" is playing courtesy of the band. And in "A Night to Remember" (1958) when a married couple walk down the grand stairs, the same song is playing.
Not really trivia, but amusing just the same. When Jack and Rose are on the deck after he saves her, Rose says the line ,"Poor little rich girl - what does she know about misery?" "Poor Little Rich Girl" was the name of a movie in which Gloria Stuart (old Rose) played a part in 1936.
Director James Cameron initially wanted Gwyneth Paltrow to play Rose, but she passed on the role telling the media is wasn't "her cup of tea". Coincidentally, Kate Winslet rejected the role of Viola in Shakespeare in Love, which eventually went to Gwyneth.
In the movie, Molly Brown is sitting in a lifeboat next to Ruth and saying something like "Plenty of room, honey" to Rose. In fact - according to Molly Brown's account of the events - Molly was walking around on deck, urging people to get into lifeboats; a lifeboat was already starting to be lowered when two men grabbed her and threw her into the boat.