Corrected entry: Leaving aside the many inaccuracies which have come to light since the discovery of the wreck, there are many details about the Titanic that should have been known to the film-makers. Including that the words "Titanic" and "Liverpool" on the stern were painted on, and not done in raised lettering as shown in the film.
Corrected entry: When the Titanic has been raised and the scientist hoists the White Star company flag, he hoists it from completely the wrong place. That flag wasn't flown from the flagstaff at the stern - it belonged at the top of the mainmast. As someone who has studied the Titanic, this scientist would surely have known this.
Corrected entry: When the real Titanic sank, the first funnel broke off and fell into the water. This was reported by many eyewitnesses, including passengers and officers. In the movie, the first funnel is intact and it is the second funnel that is broken off. I read somewhere that the movie makers did this for aesthetic reasons. Still, it is a factual error.
Corrected entry: The Soviets are trying to claim the Titanic, and they land a Soviet helicopter on the deck of the Titanic. The problem is that this Helicopter is really a U.S made Huey (like the ones flown in Vietnam) with a red star painted on the side. (Quite obviously it would be hard to acquire a real Soviet helicopter, however, this is still a mistake.)