Continuity mistake: We see the plates sliding out of the holder and smashing as the ship starts to go vertical. Then 50 seconds later we see more plates falling from the same holder. However, the positions of the plates have changed and there are stacks of plates in sections that were empty. (02:30:10 - 02:31:00)
Continuity mistake: We see Mr Andrew walking through the 1st class cabins just after hitting the iceberg. He has 4 blueprint rolls under his arms. We then see him out on deck while discussing the situation with a few other men and the rolls have gone. As he gets to the office with Captain Smith he has the rolls again. (01:39:20)
Other mistake: In the scene where Rose is sitting in front of her vanity mirror after Jack saves her life, Cal bestows upon her the 16-carat Heart of the Ocean necklace. He drapes the necklace around her neck but never actually fastens it (the camera's on him the whole time), yet it stays in place even as Rose touches the diamond and runs her fingers across the chain. A 16-carat diamond would slide right off someone's neck if it were not properly fastened.