The Missouri was active during the first Gulf War and it is not so unbelievable that the ship is capable of building up steam for a maintenance run (described as such in the film). They couldn't do a lot of fancy maneuvers (due to equipment/crew deficiencies) and had to get within spitting distance to have any chance of actually hitting the enemy vessel. Though it looked like most of the gun crew was focused at the fire director station, which could have coordinated and automatically fired all the guns together, which was good. What is unlikely is that live rounds and powder charges were stored aboard, but whatever. The vets were also more likely mostly from the Korean War or reactivation service during the 80s, early 90s, with maybe a smattering of WWII codgers. Plus they had the survivors from the Japanese destroyer and the John Paul Jones, so probably around 300 sailors, which would be sufficient for limited ship operations for a very brief period.
Earlier mention of Guided Missile Destroyers not using their missiles during the initial engagement seems to have missed that their radar was down. There was no way to effectively guide the missiles until they whipped out the water density wave buoy thing, which wouldn't have worked if comms and radar are out...again, how do you guide the missiles if you can't relay target coordinates to them or have them track on their own? According to the movie, only more primitive radio frequencies and super-science suitcase boosted comms work.
Speaking of communications. When the alien communication ship broke up and went down, it didn't look like it was being deliberately aimed at anything. It just hit skyscrapers and a portside business area during business hours. They mention 25,000 casualties in Hong Kong, which were potential numbers for 9/11 had the buildings immediately collapsed, instead of allowing for evacuation.
I quite enjoyed the film. Yeah, it was dumb in parts, but I had fun. Watching Mighty Mo' pound the ever-loving crap out of the alien command ship was awesome. And the stuff with Sun Tzu and the nerdy scientist were funny, as were the mumbled comments of the main character. I do wish they had allowed for more of the international ships to do something, though it was cool to see Japanese warships work with American ships against a common enemy for all of five minutes before exploding.
It's a shame it's doing poorly domestically, cause Transformers 3 was so fucking stupid and boring and incomprehensible, yet it made a bajillion dollars. At least I knew what was happening in this one from scene to scene.
(I did have a headscratcher over why that one alien let the scientist walk away with the suitcase comm gear after they had apparently executed the student interns. Maybe in the novelization that alien will be one of the crewmen who doesn't want to invade and crush Earth and just wants to go home. Little does he know, the next day Mighty Mo is going to flatten him because of this act of kindness.)