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: With about 20 minutes left in the movie, after they show them carrying the shell to the 16" gun, they show the gun barrel being raised to firing position and then being loaded and then fired. The Iowa class battleships 16" guns can only be loaded in the down position.
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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.
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.
Character mistake: When Hopper is being chased by the alien and he goes on deck, Rihanna goes into the control room and aims the cannon at the alien's head. Just before she fires she says "Mahalo" which is thanks in Hawaiian. It would have been better to say "Aloha", which is Hawaiian for hello and goodbye, just before she fires the cannon.
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.