When Shinoda is reading the magazine article about Godzilla, we see a very blurry close-up picture of Godzilla's mouth with lights shining on it. This suggests that it's one of the pictures Yuki took in the tunnel when she was very close to Godzilla and the lights on Shinoda's car were shining on his face. However, the movie has already established that the film negatives were ruined by Godzilla's radiation.
Godzilla and the flying saucer's sizes change several times during the course of the movie.
Katagiri asks who gave Shinoda authorization to enter the building, and Miyasaka admits that he did it. This creates an inconsistency in the American cut of the film, which deleted eight minutes of footage from the Japanese cut, as one of the deleted scenes showed the soldier who stops Shinoda talking on the phone with Miyasaka, who tells him that Shinoda is authorized to enter the building. The American version is edited to make it appear that the bombing siren distracts the soldier and Shinoda runs into the building unnoticed.
When Orga hits Godzilla in the head the camera zooms in right after the hit to see Godzilla recoil. In the shot Orga's hand is not present even thought the previous shot doesn't show Orga lower his hand.
When we see Shinoda inspecting Godzilla's footprints on the beach, Godzilla's heavy tail dragging behind him seems to have not left a trail among the footprints. Even the very first Godzilla movie included a tail trail in between Godzilla's footprints in a similar scene.
When the two men are in the lab at CCI, when they are discovering Regenerator G-1, first they view the Godzilla skin sample under a compound light microscope. Then they move directly to an electron microscope, where they poke one individual skin cell and watch it regenerate on the monitor. There are two kinds of Electron microscope, transmission and scanning. Both require the specimens to be dead (and specially prepared with a coat of metal) in order to be viewed. It is impossible for the men to have seen a Gozilla cell alive and regenerating using the electron microscope.
Early in the movie when Godzilla roars and breaks the car front windshield, it shatters into large pieces. Front windshield glass is are laminated with a sheet of plastic in the middle and won't break that way for passenger safety. Tempered glass on the sides will shatter into very small fragments so the pieces are not from there either.
The Japanese fighter aircraft launch Sidewinder air-to-air missiles against Godzilla during the battle near the reactor. Those type of missiles are ineffective vs. ground targets.
During the seldom-used areal shots of Godzilla, the greenscreen technique becomes strikingly obvious as Godzilla's feet apparently disappear even when not obscured by anything, and he doesn't even always move in unison with the camera (the camera shakes but he remains still). Finally, he is of a completely different hue than the surrounding environment.
After exiting the tunnel, Yuki looks up at Godzilla and screams, and Godzilla lets out a roar. However, Godzilla's mouth is closed when he roars.
At several points in the American version, roars from Godzilla (1998) are added in shots where Godzilla's mouth does not open.