Factual error: After the Missouri knocks the shield down, the admiral orders all aircraft launched, but the flight deck is shown in sailing transport mode, not flight readiness. Would have taken an hour or more to clear the deck and launch.
Other mistake: When Alex Hopper is being tasered and arrested for robbing the convenience store, you can see his shirt is almost clean on his back. But he fell on the bottles and sodas rack in the store, the shirt should have stains.
Plot hole: The Tomahawk Cruise Missiles the Arleigh-Burke Class destroyers carry have a range of approximately 1500km. As soon as Alex got the message from Sam, they could have blown that Saddle Ridge communications facility to kingdom come with just a few cruise missiles. They didn't need to get in range because the entire dome surrounding the Hawaiian Islands was smaller in diameter than the range of the Tomahawk Cruise Missiles. Cruise missiles have internal guidance, so they wouldn't rely on the radar, which was jammed.
Factual error: How does the main hero Lieutenant Alex Hopper even get into the Navy as an officer in the first place with a felony breaking and entering on his record? You need at least a Secret clearance and a good moral background to commission as an officer, neither of which would be something Alex can get with a felony on his record.
Factual error: By the time the survivors of the JPJ arrive on board the USS Missouri, there are less than 3 hours before the satellite is in position. When lighting off cold boilers, it takes longer than that to get steam up, yet within minutes the bridge is informed that they have steam in all 8 boilers. If it was that easy, all the battleships at Pearl Harbor on December 7th 1941 could have gotten underway immediately.
Other mistake: The shot of the fleet outside of the barrier is reversed. The Aircraft carriers landing deck is slanted right instead of left. (01:15:00)
Continuity mistake: The USS Sampson has no Close In-Weapons System at the bow when the movie starts, but uses one to counter enemy fire later.
Factual error: When the alien ship crashes into Hong Kong's Bank of China building, flaming debris can be seen flying past the statue of the Big Buddha, which was also established in an earlier shot as being located just behind the financial area of the city, Central. In reality, the Big Buddha is nowhere NEAR Central, out of view of the Peak, and not even located on Hong Kong island - but on Lantau island, to the west. The Big Buddha is also not included in the Hong Kong city skyline.
Factual error: Throughout the movie, Hopper is wearing both the silver and gold ESWS (Enlisted Surface Warfare Specialist) and SWO (Surface Warfare Officer) pins on his uniform at the same time. While it is possible to qualify both of these (one while enlisted, and the other after becoming an officer) you would never wear both of them at the same time. The officer's pin supersedes the silver pin.
Character mistake: After getting his silver star, Hopper is spoken to by a special warfare commander who has the Navy and Marine Corps medal. But the colors are reversed. The blue should be on your left, and the red should be on your right as you stand face to face in front of the wearer. The stars on some of his ribbons are also upside down. (01:53:45)
Factual error: The USS Missouri is a 68-year-old museum ship. Only a few museum ships are still able to sail under their own power. The USS Missouri, however, is not one of them, and could never have left port. There is no fuel on board, corrosion has done serious damage to the rotor blades and controls, and if one was to try and refire the boilers, they would surely explode. Also, there is no ammunition on board, plus all controls have been stripped, and all tubes and barrels blocked to prevent dirt from damaging them. Therefore, it cannot ever fire a shot again. Though it was renovated in 2010, it was mostly to prevent it from rusting away and sinking.