Okay, after Jack draws Rose he takes the drawing and writes the date April 14, 1912 on the drawing at the bottom. If the ship sank on April 14 at 2:00 in the morning, the ship would have sank already. And if couldn't have been after 12:00 because later the clock said it was 11:30. Big mistake.
Titanic struck the iceberg on April 14, 1912 between 11:30 and midnight--actually closer to midnight. The ship didn't actually completely sink until 2:05 A.M. the next morning--August 15, 1912. It states this in every historical accounting of the disaster, and is even referenced in the movie!!
The Titanic hit the iceberg the night of the 14th (11:40, I believe), but did not sink until the morning of the 15th (2:20), so what you saw was, in fact, correct. This is not a slip-up.
I wish I didn't know this, but oh well, Titanic sunk between April 14 and 15, Jack was drawing on the 14th before midnight, and it actually went under very early in the morning on the 15th.
This isnt a big mistake at all. It isnt even nearly a mistake. The Titanic sank at 20min past 2 in the morning, on April 15th, 1912. Jack drew the picture on the night of April 14th, 1912.
Get your facts straight.
Jack draws Rose on April 14, 1912. The fact is, that we don't know what time that Jack draws Rose. It could be, be a 7,8, or 9pm that evening. Jack dated the drawing April 14, 1912, because it was before Midnight. The Titanic hit the iceberg between 11 and 11:45 pm on the night of April 14, the same evening that Jacks draws Rose. The Titanic sink around 2:00am or 2:30am on the morning of April 15. The date on the drawing was right.