Continuity mistake: When Jack and Rose are running through the dining room, both of them are completely dry and running up. After Cal tells Lovejoy he'll give him the diamond if he gets it back, we cut back to Jack and Rose and both of them are soaking wet, most noticeably Jack. (02:13:15)
Visible crew/equipment: In the scene after Jack and Rose try to save the child from the Italian guy, when the water bursts through the doors, they run away from it. But take a close look at Jack's neck: you can see the edge of a black wetsuit. And under his entire shirt, it's a little darker than it is a few moments later when they try to open the gate. (02:16:45)
Continuity mistake: After Cal throws Rose's cigarette away, she lowers her hand. Then there's a very brief angle on Molly Brown where Rose is lowering her hand again up to a point where it disappears offscreen. Then a millisecond later it cuts back to Rose and her hand is magically raised and still, no sign of her lowering it, and shortly after she lowers it while Cal extinguishes the cigarette and she places her index finger on the holder. Close-up on Rose and her fingers are in the previous position and she is extending her index finger again to hide the holder. So there's actually 2 mistakes in a lapse of 3 seconds. (00:32:10)
Factual error: It's impossible that Rose would've been able to survive for as long as she did whilst wearing that thin, delicate lounging dress she changed into after Jack drew her portrait. She was in and out of the water constantly before finally climbing on top of the door frame in the water, and while the coat Cal put on her could've kept her torso warm, her legs were exposed throughout much of the ordeal. The human body can barely function in freezing temperatures, but she moves around with considerable agility until shortly before she's rescued from the water.
Character mistake: At the beginning of the movie, Bill Paxton is pulling out documents out of the safe, maybe destroying some of them. Extremely unprofessional from an archaeological perspective. Although he represents a private company on a Russian ship searching for a diamond, he for sure violates many international laws with this brutal act of recovering objects. A professional treasure hunter should know that, plus a camera is filming him. He risks never getting a licence for a treasure hunt again.
Other mistake: After the "flying" scene, the story cuts back to real time. When it starts to transition back to the flashback, the camera zooms in on a television screen with the fireplace in it. This screen is 1) also used in the beginning of the movie 2) impossible, seeing how there was only one ROV in that room, and it shows the ROV in it. (00:06:15 - 01:20:10)
Continuity mistake: About half an hour in when the rear of Titanic is shown, look at the very rear of the ship and you will see a red sign (near the triple screws) to the right of an over-hanging light. Shortly afterwards when Rose approaches the rear of the ship to jump off, the sign has now moved to the other side of the light. (00:31:50 - 00:36:15)