I found a site with all these mistakes from the Titanic on it. Its actually quite funny.
1. Visible crew/equipment: When Jack and Rose are going back to the sitting room to tell Cal and Ruth about the bad news, you can see a crew member reflected on the wall over by the door.
2. Factual error: The lake that Jack told Rose he went ice fishing on when she was threatening to jump is Lake Wissota, a man-made lake in Wisconsin near Chippewa Falls (where Jack grew up). The lake was only filled with water in 1918 when a power company built a dam on the Chippewa River, six years after the Titanic sank.
3. Visible crew/equipment: When Jack comes to the first class door for the first time in his tux, you can see a cameraman in the glass door before he enters.
4. Continuity: When Jack and Rose are going down with the ship, there is a man holding onto the flagpole. The man's life jacket disappears and reappears.
5. Other: In the beginning of the film, when Jack is running to the boat on the pier, his rucksack is a Swedish Army rucksack, model 1939, and nowadays widely sold as army surplus.
6. Continuity: When Jack and Rose finally come aboard the top of the ship after she rescues him they ask the Colonel if there are any boats left and he says "up that way" The woman on the left, who looks kind of pathetic, is then later seen on the life boat with Molly Brown. (They show her face right after Molly says the line "its your men out there") The life boat with Molly Brown in it was sent out before the scene with the Colonel, meaning that she must have gone on the life boat, swam back onto the ship and then back onto the lifeboat.
7. Continuity: When Rose and Jack run through the dining room with Cal shooting them, notice that the floor is tilted to reflect the ship sinking. In the next scene when they run down the stairs, the floor is now perfectly level. There is no tilt to the floor. Notice how the water tumbles out of the door - it falls on a flat surface and disperses evenly with no angle to it.
8. Continuity: When Rose is trying to rescue Jack she spies a fire axe. Smashing all the glass out from the holder she grabs the axe and turns round. The next camera shot shows Rose standing in front of the case with almost all of its glass intact.
9. Other: When Rose demands to be taken down in the elevator to look for Jack, the shadows cast on Rose's face are moving down. Surely if the elevator is moving down, then the shadows cast from outside the elevator would be moving up on Rose's face.
10. 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 "The Pleasure Principle." Also, up until 1919, Freud relied solely on data from females.
11. Continuity: When Jack is persuading Rose not to jump, Jack's shirt collar changes position several times, revealing his white t-shirt from a little to a lot.
12. Factual error: When Jack is handcuffed to the pipe below decks, the elbow joint is a modern welded joint, not a bolted flange joint as in the rest of the ship. I'm sure this was done to allow Jack to move about with greater ease as the water level rose.
13. Continuity: Look closely at the location of Rose's beauty-mark the first time you see her at the dock. It is on the opposite side of her face during the rest of the movie.
14. 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.
15. Deliberate "mistake": When Jack and Fabrizio are at the bow, the anchor well below them is black. Along with that, the foremost railing is not connected with the rest. But when Rose and Jack are there the well is white and the railing connects. Plus during the "flying" sequence the gap between the vertical bits of the railing is different in different shots of the ship.
There are more and I will post the link in the links spot of this spot. :)