Factual error: F-18 Hornets deploy Harpoon anti-ship missiles to destroy Madison Square Garden. The Harpoon is an anti-ship missile, designed to punch holes in ships. It is not designed, nor capable of levelling buildings. A Harpoon also works best over water; firing over a crowded city confuses its radar seeker head and leads to tracking issues.
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)
Continuity mistake: They go into the broadcast booth in Madison Square Garden. While Audrey is broadcasting, the French guy moves the vertical blinds to his left to look out the window and sees a dinosaur raise its head. Just after that the view switches to the dinosaur's side and he is now holding the blinds to his right.
Revealing mistake: When Godzilla attacks the fish market, the creature picks up the seafood/fish truck with the driver still inside. As he's being knocked out of the cab, you can see dozens of boxes set up where the truck was once parked for him to land on. (00:26:00)