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: After season 1, then Captain Chandler is shows with a Silver Star Medal. But in season 5 he does not have it any more. Considering his status in overall and the fact that he has not lost medals/awards that are considered higher, his Silver Star would not be revoked from him.
Factual error: "When we reach the States you will be charged with War Crimes and prosecuted to the full extent of the law." Despite a lot of assumptions, the USA is the only major power to have opted out of this convention. You cannot be charged with "War Crimes" in the USA. (00:05:55)
Revealing mistake: When the Americans are leaving the Russian ship they are doing it right next to a tensioned mooring line which you would only see in an harbor but not on a ship that operates under its own power in open water, thereby betraying the filming location as a docked (museum) ship. (00:35:50)
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.
Factual error: The dead Royal Navy submarine captain wears a beret. British submarine captains still wear the traditional submarine captain's white-topped peaked cap if they wear headgear at all. His cap badge also features the king's crown, which has not been worn since George VI's death in 1952, instead of the current queen's crown.
Factual error: The Royal Australian Navy special forces operator Wolf Taylor is a 'senior chief'. There is no such rank as senior chief petty officer in the RAN. The two most senior non-commissioned ranks are chief petty officer and warrant officer (the latter a non-commissioned rank and not the same as an American WO).
Continuity mistake: Chandler is reviewing the President's paperwork and finds the manifests which brought his wife and daughters from Washington (document dated 07-05-13) and his son from Detroit (document dated 08-02-13). He then checks the computer for casualty figures in Michigan where the son was originally from (dated 8/4/14-onwards). So the plague hit in early August 2014, but the documents show the family leaving their home a full year earlier. This is not a plot issue (no, they did not fly out a year prior to the plague), but rather a prop-maker error. (00:28:00)
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.