Factual error: When the ship is being launched a champagne bottle is smashed against the hull. Harland & Wolff, like many shipbuilders, did not smash champagne bottles against the hull.
Factual error: When the ship sinks it lamely slips into the water at a low angle. Somewhat of an anti-climax. Contrary to some reports, even at the time the film was made it was known that part of the ship upended at 45 degrees and sank vertically. I discovered this when I listened to an eyewitness account which is a permanent fixture at the British Library.
Factual error: In the opening scene you see the ship being launched - it has a 4 bladed propeller on the outer side, the real ship had 3 blades on each propeller. During the sinking this is pictured correctly.
Factual error: According to most if not all documentaries and scholarly articles on the Titanic when the man in the crows nest (named Fleet) sighted the berg he called down on the phone "Iceberg, right ahead!" In the movie he says "Iceberg, dead ahead." In testimony he said he said "right ahead." Right ahead is the British term, dead ahead is the American term. Fleet was British.
Factual error: The first funnel broke and killed a lot of people, not the fourth.
Factual error: At the very end, there is a shot onboard the rescue boat (that was too late). If you look in the background, you can see the boat is bobbing with the waves, by the way the water is in shot then out, then in, etc. A ship of that size would just break the waves. No way could it bob to the extent it does in the film. A lifeboat you would expect to bob that much but not a ship of that size.