Plot hole: After the nuclear missile has overshot the ship and is determined to be heading for land, a map on a computer display gives an indication of the missile's trajectory relative to the Nathan James and western Europe. After the nuclear detonation, an external shot shows the blast is to the port side of the ship, giving the impression the ship is on a southern bearing off the west coast of France. At the time of detonation, the bridge crew shield their eyes while facing the front of the bridge, which would give the impression the ship is pointed right at the blast rather than off the port side. Later, Master Chief Jeter reports that the jet stream is pushing the radiation north-northeast, as if to indicate the ship is currently sitting in the fallout zone, when this would actually be pushing the radiation cloud away from the Nathan James.
Factual error: After the nuclear detonation LT Alisha Granderson reports the ship's fuel reserves as 11% and states they will run out of fuel in less then 6 hours, even at maximum conservation. Working from published specifications (Wikipedia and www.globalsecurity.org) 11% should last them for more than 24 hours operating normally at 20 knots and one would think that maximum conservation extends this timeframe. (00:27:15)
Factual error: When Chandler is looking through his rangefinder at the Italian passenger liner, the lat-long coordinates indicated in the lower left corner of the display are quickly decrementing, meaning they couldn't possibly indicate a current GPS location. In addition, the numbers are nowhere near the coordinates Chandler gives when he attempts to hail the passenger liner ("48° north, 15° west").
Continuity mistake: While trying to restart the engines after the ship is hit by the nuke's EMP, Chandler is checking the fuses while Chung is going through his checklist. There are only five visible fuses in the six available slots in the panel that Chandler is checking. After he gives the order for Chung to "give it a kick-start," the slot which previously had no fuse now does, only for it to shoot out from the start attempt.