Go to the part of the movie in which Jack and Rose are running from Cal's goon. When they go on the elevator, Rose gives him the finger. This was not invented until World War 2 though, about 30 years too early!
English archers also used gestures such as the finger, and the "up-yours" (two fingers up) sign, whilst warring with the French. The French used to cut off the middle and index fingers of any English archers they captured (and bows were the main English weapon, so in other words, pretty much every English man they captured), so that the captive could never fire an arrow again. The English would taunt the French with the finger, and the up-yours sign, as a way of saying, "Look, you bastards, I've still got my fingers!"
So the person above is right...no-one really "invents" the sign, and as you can see several different cultures have used it independant of one another throughout history, so this is not a slip-up.