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. (00:49:25)
Continuity mistake: Godzilla noticeably changes size throughout the movie. For example, she is shown lairing in a subway tunnel, but she cannot fit into the Hyde Park tunnel (taxicab scene), which is significantly larger than a subway tunnel. Also, compare the size of Godzilla's eye next to Matthew Broderick during the fish scene and Godzilla's death scene. The eye is way bigger in the latter.
Continuity mistake: Near the end of the movie there are 3 US Navy F-18 planes. The lead plane shows a graphic of 4 missiles, 2 of which he launches at Madison Square Garden. Then later, and without landing, the 3 planes fire at Godzilla, 2 missiles from each plane on both passes. This means the lead plane fired 6 of its 4 missiles.
Other mistake: At the taxi cab chase at the end, you can notice when the car is a real one and when it's CGI. Note how the real car has scratches and other things on the front of it, but the CGI car, if you look closely, has almost no imperfections, and even if it does have some, it doesn't match the real car one bit. You can see these things when the car drives off his mouth or when you see Godzilla running behind.
Continuity mistake: When Godzilla is chasing the taxi, the taxi crashes through a chainlink fence. As it rounds the corner shortly after going through the fence, the sign on top of the cab comes loose and is being held loosely by a wire toward the front of the cab. You can clearly see that the sign is loose, but a few shots later, the sign is attached firmly in place atop the cab.
Continuity mistake: During the scene right after the F-18's destroy Madison Square Garden, Godzilla goes after the taxi and Nick tells Phillipe to turn the car around. The problem is that on the street you can see that the first time they went through, Godzilla left some huge footprints and destroyed the street. When they turn around and drive up there a second time, the street is perfect. This happens again when they are stuck in the Hyde Park Tunnel and Godzilla shoves a claw into it and breaks up the road right in front of the taxi, but when Phillipe drives forward and then puts on the highbeams, the road is fine.
Continuity mistake: As Godzilla is about to step on Animal, we see two cars are directly behind Animal (a yellow taxi and a gray car). Each shot of Animal from the front as the monster approaches (and he's trying to get the tape locked into the camera) shows portions of the cars. But in the side shot of the foot as it lands, no cars are right behind Animal at all. (00:29:50)
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. (00:33:35)
Other mistake: When they are tracking Godzilla to the second pile of fish in Central Park, the tracking device says that Godzilla is moving with a speed of 175 mph. If you look at the shots before it with the soldier looking over the top of the building, it is impossible for her to walk at that speed. (01:18:15)
Revealing mistake: When they are climbing up from the subway tunnel into Madison Square Garden, there are lots of half-dead fish scattered around from when Godzilla was feeding. Right before they enter the arena, in the overhead shot looking down on the actors, there is a wiggling fish in the lower left portion of the screen. If you look closely, you can see a string attached to the fish. A crew member is obviously tugging on it from below, to make the fish move.
Continuity mistake: The first footprint - the one Nick is standing in - is clearly smaller that those shown from the helicopter (watch the toes). (00:11:05 - 00:12:25)
Continuity mistake: When Nick has first contact with Godzilla, he signals to the soldiers that they should not shoot. How the soldiers can see from that far and in the heavy rain what his fingers are pointing is one question, the bigger problem is that when we see a close-up of the guy's fingers, there's no rain.
Other mistake: It's difficult to spot (it's easier on DVD, but I don't have the timecode). Godzilla has just left Central Park after suspecting the trap with the fish. As she rumbles down the street, hundreds of Apache helicopters swarm in and attack. When they begin firing their cannons at Godzilla, if you look carefully, you'll see the tracer fire from one gunship overlap over another gunship. The cannon fire is heading away from the camera and getting smaller, so it should at least go through the other helicopter and disappear on the other side, but it remains superimposed on the Apache. A little special effects mistake.
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 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.