As an active duty Navy guy on an Arleigh Burke class destroyer I noted a couple things and have some answers to questions above.
First,
Except the first salvo came towards the front of the ship and newer DDGs are lacking a forward CIWS mount.
Next,
Covers are optional for all hands while underway. Additionally, we generally do not salute underway except for special circumstances i.e. award ceremonies and formal events. As for the captain saluting without his cover... the CO does what he wants, I've seen it done before.
This happens. Honestly, a lot more often then you'd think. Some ships ban relationships period others just say keep it off the ship and on your own time but this definitely doesn't stop everyone.
The problem is curvature of the earth and how far above the deck their flying at. They quite literally can fly below the view able plane. On how far we would see them, I can't say but still at 24 nm and traveling at 150 it would be nearly 10 minutes before they got to the ship which is forever in a combat situation.
They wouldn't. Enough said.
There's a laundry list wrong with this scene but if things where to blow like that, they were probably down to the last one after the dozens they already replaced from the cascade faults. I do have to say though, electrical safety gloves?
The biggest flaw that nobody has really mentioned yet though is how the hell they stayed out for four months without an unrep(underway replenishment) for fuel and food. The ships sustainability without outside support is nowhere near that long. At the very least the unrep ship would've given them the scoop on what was happening.
Anyway, upsides, it does have some cool Navy footage that's exciting to watch. I'll give the show a few episodes and see how it goes.