Other mistake: It's difficult to spot (it's easier on DVD, but I don't have the timecode). Godzilla has just left Central Park after suspecting the trap with the fish. As she rumbles down the street, hundreds of Apache helicopters swarm in and attack. When they begin firing their cannons at Godzilla, if you look carefully, you'll see the tracer fire from one gunship overlap over another gunship. The cannon fire is heading away from the camera and getting smaller, so it should at least go through the other helicopter and disappear on the other side, but it remains superimposed on the Apache. A little special effects mistake.
Other mistake: When the first fish trap is set up and Nick realises that the manhole covers need to come off, the first covers come off, with the pile of fish in the background about one block away. Nick then runs another 1/2 a block to a block to remove another manhole cover before Godzilla sticks his head up through the road. Taking into account Godzilla's size, we can assume she is about 3 blocks away from the fish. When the shot cuts to the computer screen in the command centre, it indicates that Godzilla is SIX blocks away from the fish.
Factual error: The ship shown in the film is a dry-bulk carrier, not a fishing vessel.
Revealing mistake: When the two soldiers are in the subway tunnel just before Godzilla's eye opens at the end of the tunnel, check out the beams on the flashlights. When the flashlights shine on the walls of the tunnel, they are normal. When they shine FURTHER AWAY onto Godzilla, the light beams get narrower and more laser-like. The circle the light makes on a surface loses the dark circle in the centre when it shines on Godzilla too.
Factual error: The giant footprints in the movie are obviously dug out of the ground. If they were real, the ground would be heavy compressed in a footfrint shape. These look like they were dug with a foot-shaped shovel.
Factual error: The Apache gunship helicopters seen in the film have three weapons pylons under each wing. In real life, Apaches have only two pylons under each wing. It's possible the makers of the film gave them the extra pylons to make them look "cooler".
Other mistake: Operations on the ground in Manhattan appear to be under the command of "Sgt. O'Neal." Such a sizable operation would never be placed under a sergeant, but would more likely be commanded by an officer, such as a captain or a major. Also, O'Neal is repeatedly called "Sir" by other soldiers. A sergeant would never be called "Sir."
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."