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.
Plot hole: Chandler chooses Granderson as his XO over Cameron Burk, partly because Burk made an error of judgement and partly as Granderson has been with him since the beginning. However, he completely overlooks the navigator, Lt Mejia, who is a highly competent officer who has also been with him since the beginning and has considerable seniority over Granderson (but is a recurring character as opposed to being on the main cast). While much is made of Burk being demoted, nobody says a word about Mejia being passed over.