(at around 1h 10 mins) When Niko is in the taxi and is asking where Philippe is taking him, Niko's lips don't match up to what he's saying. For example when he says "Let me go!", his lips do NOT match what he's saying.
(at around 20 mins) Elsie suggests that Godzilla's footprints may belong to the dinosaur Allosaurus, and Nick corrects her that Godzilla is much too big to be a dinosaur. A true paleontologists wouldn't have considered this in the first place, as Godzilla's footprints are already larger than most dinosaurs. It's also impossible to determine the genus of a dinosaur from just a footprint, so Elsie's guess couldn't have been any more specific than a "theropod dinosaur" (bipedal carnivorous dinosaurs).
Although Godzilla's size remains mostly consistent throughout the film (with the apparent size changes being illusions given by camera tricks) there are still a few instances where it does change: examples are the scene where Godzilla's eye opens behind a soldier and one of the shots of its appearance during the first fish bait sequence.
(at around 11 mins) The very first footprint (the one that Nick walks into) is clearly from a different animal than the ones that followed. The footprint is rather solid pad-like with protruding toe-like appendages whilst the ones that followed it are more talon-based phalanges or fingers. Much like the differences from an elephant's foot and a bird's. This is also the only time this footprint takes place.
Throughout the chase scene near the movie's end, the advertisement light on the taxi roof is on/off between shots. In addition, sometimes it appears firmly fixed in place, while at other times it is obviously loose and sliding all over the roof.
(at around 27 mins) When Godzilla is approaching the News Studio the light inside is shaking, yet when he is right outside the window and still walking at the same pace, there is no vibration or shaking of the light.
(at around 1h 9 mins) When Niko character leaves town in a cab we see pouring rain through the plain-glass rear window of the cab. Later, when the cab stops to reveal the driver as French secret service, we see the rear window over Broderick's shoulder suddenly now has defroster wires embedded in the glass.
(at around 11 mins) When Dr. Niko is standing in his "sample" (i.e., the footprint), Colonel Hicks uses a ladder to climb out of the footprint, but they never descended a ladder to get into the footprint in the first place. A long shot of the scene reveals that all sides of the print are vertical - there is no sloped side that they could have walked down.
Upon showing the aftermath of Godzilla's first attack on New York there's a shot of the MetLife building with a huge hole torn right through the middle of it. But later there's a wide shot of the city showing the MetLife building completely intact.
The cargo ship seen washed up on the shore after Tatopoulos examines the footprint is different to the ship attacked at the start of the film. The ship at the start has a single superstructure at its rear, whereas the washed up ship has front and rear superstructures.
(at around 1h 55 mins) During the final taxi chase sequence we see Godzilla run by a Carl's Jr. billboard. All Carl's Jr. franchises in New York are called Hardee's, revealing that the scene was shot in L.A.
Godzilla approaches Manhattan from the open ocean, crosses the FDR Expressway, and makes first contact at the Seaport District. However the fish markets and the district sit near the East River and across from Brooklyn. Moreover, Manhattan does not directly sit on the open ocean and is surrounded on almost all sides by relatively narrow bodies of water.
(at around 2h) After Madison Square, characters drive toward the Brooklyn Bridge because it's "the closest suspension bridge" to their location. In fact, they'd have to pass the Williamsburg and Manhattan Bridges - both suspension bridges - to get to the Brooklyn Bridge.
The missiles used do not have enough explosive power to blow the top off the Chrysler building. Additionally, the missiles do not have the power to destroy Madison Square Garden in such a huge explosion with just two shots.
"Cold blooded animal" does not mean its blood is cold; it means it does not regulate temperature by itself. To move a mass of that size, you would need a lot of energy and you probably would dissipate a lot of heat (this goes for the tracking missiles, and the fact that the animal seems to move very fast in cold water). Also, it would probably be easy to track on land with seismic triangulation.
Jet aircraft cannot fly so close behind each other when in a line formation; the engine exhaust from the first Jet would extinguish the seconds jet engine, having momentarily eaten up all the oxygen in that path.
(at around 7 mins) The military helicopter that picks up Tatopoulos from Chernobyl at the beginning of the movie is an American built Piasecki H-21, known also as "flying banana." However, neither Ukraine nor the former USSR ever possessed or used this type of helicopter.
(at around 1h 24 mins) The officers aboard one of the submarines wear caps reading "USS Utah SSBN 745". "SSBN" refers to ballistic missile submarines, which are large, heavy and slow, therefore unsuitable for pursuit tasks. A fast attack submarine (SSN) would make more sense.
(at around 2 mins) The opening sequence shows some mushroom clouds and captions telling the viewer they're looking at French Polynesia. The French nuclear program existed only of subsurface explosions. The explosions shown are actually American nuclear tests from the fifties.
(at around 20 mins) During the flight to New York, Dr. Elsie Chapman suggests that the beast is a "sauropoda Allosaurus." A true paleontologist would know that the Allosaurus was a theropod, not a sauropod.
The AH-64 Apache helicopter does not have a machine gun mounted
on its "cheeks" The 30mm chain gun that it carries is located under the cockpit, on the chin of the helicopter. Also, the muzzle flash from the guns mounted on the side would interfere with the pilot and the gunner's night vision.
On the Battle Dress Uniform of Colonel Hicks he displays two ranks. A silver oak leaf cluster on the left collar (lieutenant colonel) and an eagle on the right (colonel). No military personnel can have two ranks simultaneously.
(at around 1h 50 mins) When fighters are locking onto Madison Square Gardens with their missiles, they say "Selecting LGB's" (Laser Guided Bombs). On the screen the pilot is looking at it says "Weapon AGM-84 HARPOON (2)." Harpoon is a radar-guided anti-ship missile, not a laser-guided bomb. Later the F/A 18s are commanded to release their Mavericks, yet another type of missile - primarily an anti-tank weapon.
At the end of the movie when Godzilla is chasing the cab across the Brooklyn Bridge, the bridge only has 2 suspension cables (1 on each side) whereas the real bridge has 4 (1 on each side and 2 running down the center).
Colonel Hicks is wearing the branch insignia of the Army's Office of the Inspector General on his lapel. The IG basically performs non-combat inspections and audits on Army units. The commander of a combat operation would be an officer from a Combat Arms branch (Infantry, Cavalry, Special Forces, etc.)
In the cockpit, we see that the machine guns fire in pairs; Apaches only have one automatic cannon. Also, from an outside view, we can see the fired rounds coming from the wings; the Apache's gun is mounted underneath the nose.
Near the beginning of the movie a reporter says New York has seen more damage than the World Trade Center bombing. But in the next scene the Twin Towers are still standing. The reporter is clearly referring to the 1993 World Trade Center bombing which failed to destroy the towers, not the September 11, 2001 attacks.
(at around 1h 24 mins) After Godzilla jumps in the water, in the first scene when the camera passes by the first submarine, an American flag is clearly visible painted reversed onto its hull. No submarine in the US Navy, or any other navy, have flags painted on them.
(at around 14 mins) When Nick is talking to Dr. Elsie Chapman during the jeep ride in Panama, it is obvious that the whole scene was filmed on the same short stretch of road; the same characteristically tall, slender tree can be seen behind both actors several times, in both the shots and reverse shots.
(at around 47 mins) When Nick approaches the feasting Godzilla from behind, there is a group of soldiers running around a Humvee to the right who seemingly pop into existence between frames. They don't appear to have been properly rotoscoped, so Godzilla's animation overlaps them, even though the monster is supposed to be in the background. In fact, their reflections on the wet ground can be seen before they appear.
The goof items below may give away important plot points.
(at around 55 mins) When Nick buys the home pregnancy test, one of the boxes given to him by the pharmacist is a "Duane Reade" brand box. Dunae Reade is a large chain of drugstores in NY that sells their own brands. Small drugstores do not sell the Duane Reade brand.
Most of the last hour of the movie is concerned with trying to keep the baby Godzillas contained inside Madison Square Garden, but they seemingly ignore the fact that there's a huge hole in the floor of the arena leading to the sewers. The team's original plan was to blow up the eggs with explosives, thus erasing any further concern (as they would be obviously destroyed). The problem rose when the eggs hatched and some of the baby Godzillas not only began attacking the team, but also destroyed the detonators needed to activate the explosives. The remaining men literally could not do anything in regards to the hole.