Factual error: The Apaches in the film are depicted with dual machine guns on each side of the cockpit, mounted directly on the windows. In real life, Apaches cannot mount such cannons, and instead use an M230 Chaingun in a turret underneath the helicopter, which the film Apaches have, but for some reason do not use.
Factual error: The guys in BDU's (camouflage) have their sleeves rolled up with the lighter colored inside material showing. They are supposed to be Army soldiers. Only the Marines roll their sleeves this way. The rest of us can roll our sleeves up but have to fold the outer layer in a way that the darker camouflage material is still showing.
Factual error: Another CG versus physics problem: When the creature attacks the helicopters from the back, it eats one and the remaining two try to escape. However, the helicopters accelerate at least twice as fast as they would be able to in real life - they start from being still in air and they reach a circa 60kph speed in under two seconds.
Factual error: When Godzilla first attacks New York and then disappears, we are shown the MetLife Building, which has a massive gaping hole in it. The immense structural stress of a gigantic lizard smashing through the building, not to mention most of the center supports being taken with it, should have collapsed the building, yet it still is standing.
Factual error: When the F-18s are inbound to Madison Square Garden, the lead pilot arms a pair of AGM-84 harpoons, but he says he is arming LGBs, which stand for Laser-Guided Bombs. Harpoons are not laser-guided, they are radar-guided sea-skimming anti-ship missiles, which make them impractical for destroying a building.
Factual error: A sergeant is neither called sir nor is saluted. Sergeant O'Neal is called sir twice and saluted twice. The first time is shortly before they dump the fish for bait the first time. Someone runs up to O'Neal, says sir and salutes him. He says something about ten minutes then salutes him again and runs away. The second time is when O'Neal is on the roof and looks over the parapet and sees Zilla walking past. Right after that someone comes up to him and says "Sir, Godzilla has been spotted in section five."
Factual error: When Matthew Broderick teams up with the French Commandos and they are driving into the restricted area - when the French Commando says gum chewing makes them seem more American - they stop at the guard shack. Matthew Broderick leans forward to answer the guard who tells him "I wasn't talking to you, soldier!" In a military vehicle, the highest ranking person sits in the front passenger seat (where Broderick was sitting). The driver is just the driver - usually the lowest ranking member in the vehicle. There is no way a soldier would tell who is probably an officer to be quiet so they could speak to a private driver.