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: Dr Scott's official personnel record shows that she received her only medical degree, an MD, from Cambridge University. However, British universities do not award an MD as a first medical degree; in Britain, unlike the USA, this is a very prestigious (and rare) postgraduate research degree only awarded to very highly-qualified doctors. The medical qualification degree at Cambridge is an MBBChir (Bachelor of Medicine and Surgery), which is equivalent to an American MD. Although Americans expect doctors to have an MD, it is extremely unlikely that an official personnel record would give false information. The record also shows that her first degree was a BS in chemistry from Oxford. Oxford does not award a BSc degree (as they are called in Britain); most of its undergraduate degrees, even in science, are BAs.
Factual error: Ruskov introduces himself as a vice-admiral. However, he wears the sleeve insignia of an admiral of the fleet, two ranks higher: a wide stripe and four regular stripes (instead of the wide stripe and two regular stripes of a vice-admiral). On his epaulettes he wears the four stars worn by an admiral of the fleet until 1962, instead of the single large star of a modern admiral of the fleet or the two regular stars of a vice-admiral. Given Ruskov, it is inconceivable that he would reduce his own rank or wear the insignia of a higher rank but not use it.
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.