Revealing mistake: You need to watch carefully for this as it's tricky to spot, but it is visible without the need of slow motion. When the steward calls for the gate to be unlocked to the third class passengers, the gate is already open and just pushed to a close. You can see the gate wobbling and separating around the lock area. Also as the gate is unlocked we see a key being pressed against the lock to unlock it. However the key doesn't actually engage with the lock, making it impossible to open it. (02:02:50)Ssiscool
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.