Joe says he's come up with an idea to detect objects far away, which he calls Radar, but the idea of Radar was already invented in 1904, years before the 1912 sinking of the HMS Titanic.
Even though Dave tells Mr. James the ship is going at 15 knots (a little over 17 MPH), when Dave goes into his office you can see the ocean out of his window and the ship isn't moving at all, betraying the fact photographs of the ocean were used on the set rather than video.
Even though the desks slide across the floor to indicate the ship is tilting during sinking, none of the smaller items on other desks that would slide off, like pencils, move at all, indicating the desks were rigged to move across the floor.
When Dave looks out his window at the night sea, it's clear it is a picture since the water is not moving at all