The scene where Mark and Sofia are in bed starts with Mark laying on his back, but when the camera angle changes--without any time having elapsed--Mark is laying on his side.
While the story of Olympic running into a severe storm is true, everything else in that story isn't. Olympic encountered severe weather and was thrown around a lot by the waves. However, it never "limped to New York", nor did it need any repairs done to it. There weren't even any injuries among the passengers.