The ship they travel on is the Gigantic, referred to in the newspaper as a Cunarder. In fact Cunard names ended in -ia (e.g. "Mauretania"), while White Star names ended in -ic (e.g. "Olympic").
During the "sunset of happiness" shot, the ocean waves are going in reverse, showing the film has been run backwards.
The sun sets in the west, yet the action takes place on the East Coast, so where were the family when looking into the sunset?