Surprisingly all of the Navy stuff I saw with the exception of the Battleship at the end looked legit. From the Uniforms, the Weapons, and the Ships.

Plot looks stupid though.

I always loved when I played the game as a kid and the Alien Ship would rise out of my Game Board, create a dome over my house, then shoot bombs into the side of my plastic ships.

Correct, no Battleships are commissioned in the US Navy.

A little history on the last one.

Quote:

USS Missouri was ordered in 1940 and commissioned in June 1944. In the Pacific Theater of World War II she fought in the battles of Iwo Jima and Okinawa and shelled the Japanese home islands, and she fought in the Korean War from 1950 to 1953. She was decommissioned in 1955 into the United States Navy reserve fleets (the "Mothball Fleet"), but reactivated and modernized in 1984 as part of the 600-ship Navy plan, and provided fire support during Operation Desert Storm in January/February 1991. Missouri received a total of 11 battle stars for service in World War II, Korea, and the Persian Gulf, and was finally decommissioned on 31 March 1992, but remained on the Naval Vessel Register until her name was struck in January 1995. In 1998, she was donated to the USS Missouri Memorial Association and became a museum ship at Pearl Harbor, Hawaii.

tl;dr
The last Battleship was Decommissioned in 1992.

I've been in the Navy since 2004, and I promise, we had no Battleships. They are LONG gone, made totally ineffective due to Aircraft and Missiles. The Main force of the US Navy Fleet consists of Aircraft Carriers, Cruisers, Destroyers, Amphibs, and Frigates.

Shown in the video at time 0:10-12 first is a Destroyer, then a Cruiser right behind it.
The ship at 0:34 is horseshit unless they're on a Battleship turned museum.
0:51 - Duh, Aircraft Carrier.
0:54 - Front of a Destroyer.

Something else I thought that was cool, was at time 1:50 whoever that is, is shown wearing the brownish flash hood around their neck. When we go to General Quarters (Battle Stations) we really do put those on, (except pulled up over your head and face) and not shown are the long white gloves also we wear. All fire retardant.

At 1:57, that R2D2 looking gun is real. We had one on my last Ship. It's called CIWS (Close In Weapon System) It's a 20 mm (0.79 in) 6 barreled M61 Vulcan Gatling Gun that fires up to 4500 rounds a minute. Primarly used for Anti-Missile defense. It's really a last defense sort of thing, since it only has about a 3 mile range, and you really don't want missiles getting that close.