Factual error: When Jack and Rose begin to evacuate to the Titanic's stern, there should be only two lifeboats left on the ship: Collapsible A (which Cal was on) and Collapsible B (the overturned one with all men on it). However, if you pay attention you'll notice two other boats still there. One is still loading and another is in the water but still attached to the falls.
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.
Factual error: A point is made in the movie, and it is well known, that the water temperature of the ocean where the Titanic sank is near freezing, and at the end after it sinks, the people in the water only last a few minutes before going into an unconscious stupor and then dying. but on the boat, as it is taking on water while it is sinking, Jack and Rose are running around in this freezing water for what seems about 30 minutes with no apparent ill effects. The water could not have been heated substantially, and they simply could not have lasted nearly as long as they did running around in this water as the movie showed without slipping into unconsciousness. (02:38:30)