I watched the first three episodes this week. The first episode or two, I was constantly and verbally exasperated with the characters, who constantly muzzled each other as they went about with their weapons. I thought, "Well, maintaining an accurate depiction is, again, apparently not the goal here." Then they institute a training day where an officer yells at a sailor for muzzling his buddy. I was like.
I don't expect movies or shows to be perfect in regards to weapons handling (it's not perfect IRL in combat, either). However, I do expect a good faith effort to show responsible weapons operation. If The Last Ship continues doing it the right way, I'm hooked.
Plus, Rhona Mitra is hotter than hell, with an exotic accent to boot.