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.
The Last Ship (2014)
1 plot hole in Shanzhai - chronological order
Starring: Adam Baldwin, Rhona Mitra, Eric Dane, Travis Van Winkle
Character mistake: The Captain yells to Tex to man the "Fifty cal" but Tex goes to a mounted M240 7.62mm weapon.