In the still photo montage that opens the movie prior to the main titles, a photo supposedly depicting the fictional cornet player "Graham Farley" (there was no brass in the Titanic's small string band) is actually from a 1917 publicity shot of The Original Dixieland Jass[sic] Band featuring cornetist Dominic "Nick" LaRocca.
Pitt has just come from a meeting where the secrecy of the mission has been stressed, and the decision is clearly stated that no outsiders should learn about the project. But John Bigalow seems to already know before the news is leaked, and asks Pitt to put back the Titanic's pennant when the ship is raised.
When the team examines the horn retrieved from the wreck, they note that the instrument was presented to its owner after "three years service on the Olympic". The RMS Olympic, the Titanic's sister ship, was launched in 1910 and entered service in 1911. No one could've served 3 years on it by 1912, when the Titanic sank.
In the film, the Titanic is towed to New York from mid-ocean by harbor tugs, not ocean tugs. The towing methods are meant for harbors and other relatively calm waters, and would be very dangerous at sea.
In the film, the Titanic's second funnel is missing. Though no one knew at the time that the ship had lost all 4 funnels when it sank, it was generally known that the first (forward) funnel, not the second one, had toppled over and detached from the ship during the sinking.
Sandecker tells Pitt that they "got all the stuff from the White Star Line; engineering drawings and a complete structural design for the Titanic." White Star Line merged with Cunard Line in 1934, becoming Cunard White Star, Ltd. By the end of 1949, Cunard acquired the rest of White Star's assets, and changed its name back to Cunard. No ship has flown the White Star flag since 1968. Furthermore, at the time of the film's production the blueprints and drawings for the Olympic and Titanic were believed to have been destroyed when the Luftwaffe bombed the Belfast shipyards during WWII. A surviving set of structural blueprints for the Olympic class was discovered in the late 1990s.
When the Titanic sank, its masts and funnels were ripped off and the Grand Staircase's dome imploded. The damage was discovered in 1985, when the wreck was found. It was unknown when the film was released in 1980, and when the novel was published in 1976.
The Titanic broke in two as it sank, and the stern section suffered major structural damage, perhaps due to implosion from water pressure. However, those facts were only discovered when the ship's remains were found in 1985. Eyewitness testimony soon after the sinking was conflicting. In 1980, it was generally accepted that the Titanic sank intact.
Bigalow orders a pink gin, which is prepared by warming a brandy glass with your hands, adding a few drops of Angostura Bitters, shaking them out, then adding a single or double optic measure of gin. The glass would never be so full or so richly colored.
The goof item below may give away important plot points.
When the Starfish accidentally exceeds the 12,000-foot depth limit, it takes several minutes to leak, flood, and implode. A submersible that sprung a leak at that depth and pressure (>600psi) would implode in seconds. Also, such a blast, having the effect of a depth charge, would have destroyed or at least severely damaged the other submersible, which would have to be very close (less that 6 feet) to get a visual contact at that depth. Yet, her occupants do not feel anything.