Ok, yes - instant re-commissioning of an old Battleship is a major gap in realty but we are talking about a movie titles Battleship in an era where we have no modern battleships so I let that one pass (and the scene where all the old salts are standing on various high points of the ship always causes the dust in the room to get in my eyes).
But, I must overrule some objections. It's entirely possible that an alien civilization may have large ships that are incapable of landing and operating on land - though they did have smaller craft that could - these aliens had special helmets to cut down on the light of the sun - one conclusion that could be drawn is that they come from a dark planet - but since they have specialized helmets that allow them to venture in to the sun, I would suggest that they might live either underground, or, since they have ships that move so well in water and can't land on land, that they live under water, where it would also be dark - a water based civilization would have large craft that operate in water with smaller landing craft for land based operations.
It's been a long established tradition in Science Fiction writing that there could be civilizations who invade and destroy everything without taking "booty" or slaves - I call your attention to the Hitchhikers Guide to the Galaxy where Earth is to be utterly destroyed to put in a new space highway. This invasion was by a vanguard who lost their communications ship and was trying to re-establish contact with their fleet to bring down the real destruction - perhaps terraforming the planet to meet their needs or perhaps just to plunder some resources. Maybe they were there for the booty but didn't have time to get it - and if they were going to terraform or just plunder, they might not have need for an "insignificant" species like ours for slaves.
And that insignificance could be the answer as to why the heroes could retrofit the Missouri - they have defeated us and we could be ignored.
As for the Cartesian coordinate tracking - what better way to try to track vessels that are invisible to more modern means of detection - it's yet another example in the movie of how the old-fashioned ways of doing things can still be useful - besides, it's a movie based on a classic board game that uses Cartesian tactics - I thought it was cleverly done.
But too each their own - you can show your boys The Sound of Music, Black Beauty, Babe, Mulan, Life is Beautiful or The Empire of the Sun if you want.