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.
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)
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.
Continuity mistake: Watch the roads during the chase scenes. They go from soaking wet to dry to wet again scene to scene, in the same street as they turn around.
Continuity mistake: In the scene when Victor is chasing Nick after crossing the airport sign on the road, you can see the steering wheel of the van is being held in Victor's right hand from his point of view inside the news van, but in the next shot Victor is holding the steering wheel with his left hand. (01:09:40)
Continuity mistake: Nick and company are in a plane after leaving Tahiti. A soldier goes up to the colonel and tells him about the fishing trawlers that were pulled under. Just after that, the camera shows three guys sitting down that look up. In the following shots those guys are gone. (00:19:50)