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.
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."
Continuity mistake: When the reporter is chasing Godzilla in New York, just before he stops his hat falls on the ground between him and a taxi. But in the next shot of him when Godzilla is about to crush him, the hat is gone and is never seen again.
Factual error: At no time does the military use standard radio protocol such as "over", "out" etc.
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.
Suggested correction: There is a variant of the AGM-84 Harpoon called the "SLAM" (Standoff Land Attack Missile) which is a harpoon variant used for surface targets. Its designation is the AGM-84E. Also it's guidance system is an active radar homing system which is perfect for pretty much any targeting, not just over water. It is used on Phoenix AA missiles, Hellfire Air-To-Surface missiles and the very famous Patriot SAM missiles. Plus the SLAM even uses GPS.
Continuity mistake: In the scene where Mathew Broderick is loading his luggage into the taxi, Hank Azaria is seen opening and holding an umbrella. When he crosses the street to steal a truck, he drops the umbrella, but on the wide shot that soon follows, there is no umbrella on the ground.
Continuity mistake: When Godzilla goes to eat the pile of fish, it only takes about 3 mouthfuls from the top of the pile before being chased off. In the later shot, all the fish have been eaten.
Continuity mistake: When Viktor and Audrey fall from the ventilation ducts, Viktor's camera goes skidding across the floor about 6 feet or so away, yet when Jean Reno comes over to step on the camera it is within a foot of where Viktor fell.
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.
Continuity mistake: In the scene when Godzilla is attacking the three fishing trolleys, the big light posts fall over. When they hit the ship decks, the impact breaks the bulbs and the lights go out. However, a few shots later, as the ships are going under, the fallen lights are back on.
Suggested correction: Sergeants, just like any other military member of a higher rank than the person doing the saluting, are called sir as well as saluted.
Not true. Sergeants are non-commissioned officers. They are respected for experience and expertise but they are not saluted first or called Sir. (Some services will have Drill Sergeants or Platoon Sergeants addressed as Sir by recruits in basic training but that's not happening here).