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.
Continuity mistake: At the scene when Hopper is playing soccer he receives a kick to his face, however the blood on his face changes between shots.
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.
Other mistake: The shot of the fleet outside of the barrier is reversed. The Aircraft carriers landing deck is slanted right instead of left.
Factual error: 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.
Continuity mistake: When Hopper climbs to the roof of the convenience store, the time displayed in the upper left corner of the screen (presumably a video surveillance camera) goes from 12:11.57 to 12:12.12, then back to 12:11.36.
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.
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: When Hopper orders to drop the port anchor during the final battle, the chain changes between being stretched and taut from scene to scene.
Factual error: During the ITV News "UFO Landing Confirmed" breaking news scene, the lower caption shows the text "Amateur footage confirms rumors". ITV News is a British news network and would spell 'rumors' as 'rumours'.
Continuity mistake: In the scene on the mountain where the Hawaii police ask Mick and Sam to leave the mountain. Mick and Sam ask why and they are told during the conversation that the aliens have blocked all cell phones, radio and internet but in the next scene with the police they use a radio to communicate with each other.