Factual error: In scenes from the oil rig there are shots that show the shore line. This oil rig is supposed to be offshore of Louisiana. However, mountains can be seen in the shots of the shoreline. There are no mountains in Louisiana.
Factual error: A projectile is shown being loaded for firing. It has a light blue casing. Light blue casings denote a practice shell, not a live shell. (00:05:05)
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)
Continuity mistake: In the previous episode, Doc Rios says he can hardly see anything without his glasses. In this episode, still without his glasses, he looks out of the hut window and describes the compound beyond in detail.
Factual error: Astute class submarines do not carry ballistic missiles, much less 26 of them. (An Ohio-class, by comparison, carries 24).
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.
Continuity mistake: They are in a minefield. The map shows it's between a bunch of islands or small landmasses. All the dialogues and maps reflect this, but the visuals show open sea.
In the Dark - S3-E7
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)
Two Sailors Walk Into a Bar... - S1-E8
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: Commander Garnett, previously the chief engineer, becomes executive officer and starts wearing the line officers' star above her rank rings. This does not happen. An engineer is not trained to command a ship.
