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: The mayor is giving a speech as Godzilla arrives in NY. There are five microphones in front of him. They move between shots, most noticeably the blue and yellow ones in the middle. (00:26:30)
Trivia: There's a statue of the alien from Independence Day on top of the computer monitor in the broadcasting booth at the Madison Square Garden. (01:44:25)
Answer: Everyone was so focused on the nest in the Garden, they all forgot about Godzilla.