When they order the second attack against the Planet X people, the speaker-array on one of the trucks changes position between shots.
Despite that it takes 43 minutes to send a radio signal to Jupiter & another 43 to receive a response, the astronauts are speaking with mission control without any delay at all.
At different times in the film, characters refer to 'hydrogen oxide' as being water. This is technically incorrect, as the most common proper chemical name for water is dihydrogen oxide, since one molecule of water consists of two hydrogen atoms and one oxygen atom.
In several shots, the track on which the military vehicles move, along with support beams holding them in place can clearly be seen. In some cases these supports hold the vehicles up so high that their tires don't touch the ground.
In one of the shots of the tanks firing at Godzilla and Rodan, a "glass" window in the background keeps wobbling as if made of a sheet of thin plastic.
In the final battle scene between Godzilla, Rodan and Ghidorah, one of the buildings destroyed say "New Kirk Motors". This is footage from Mothra and is a mistake because the battle takes place in Japan not in New Kirk which is in the fictional country of Rolisca.
The American version misspelled director Ishirô Honda's name in the opening credits. Instead of Ishiro the American version credited him as Inoshiro Honda.
When Rodan first appears from the volcano, there's a distinct Godzilla roar, instead of Rodan's sound.
In several scenes the strings holding Rodan, Ghidorah and the flying saucers are clearly seen.