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.
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.
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.
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)
Sea Change - S3-E8
Factual error: They have EOTech or similar holographic sights mounted on their rifles, but "scope in" with a night vision sniper rifle scope of some kind to take out the two targets. The EOTech holographic sights are not night vision, nor have the magnification and reticle that was used in the show. (00:17:50)