Revealing mistakes: You can see the wires leading from the planes as they attack Gojira.
Crew or equipment visible: When the mother is holding her three daughters... when the camera dollies in closer, you can see its shadow.
Crew or equipment visible: When it shows the people run down the alleyway, and Gojira walks by, you can see two people run out in front, look at the camera, and really quickly lean up against the wall.
Crew or equipment visible: The scene where the mom is in the corner of the building with her daughters, telling them they'd be seeing Daddy really soon, when the camera tracks in, you can see its shadow cast on them.
Factual errors: Dr. Yamane, Japan's leading paleontologist, tells the council meeting that the Jurassic Age was two million years ago. He was only off by 142 million years.
Factual errors: Trilobites didn't live in the Jurassic Period. They lived from the Cambrian (540 mya) to the Permian Period (250 mya).
Miscellaneous: It's nine years after the dropping of atomic bombs at Hiroshima and Nagasaki, but the "authorities" cannot recognize radiation burns.
Continuity: When the Yemane's arrive on Odo Island, Emiko is wearing a skirt and Doctor Yemane is wearing a suit and a tie. However, a few minutes later Emiko is wearing slacks and Doctor Yemane's tie is gone.
Revealing mistakes: In the close-ups of Godzilla's head and upper torso as he's breathing fire, it's obvious that he is a hand puppet, and a pretty bad one at that (notice how small his arms are, and how big and round his eyeballs are, compared to the full-size suit).
Revealing mistakes: The buildings attacked by Godzilla in the model shots, from the way they "slide" on their bases and explode upwards in one whole piece, do not appear to have any foundations (or, indeed, to be fixed to the ground in any way at all).
Miscellaneous: The American actor who dubbed Dr. Yamane is the U.S. version keeps pronouncing "phenomonon" as "phemononom".
Revealing mistakes: When the jets attack Gojira as he's walking out to sea after destroying Tokyo, the rockets they fire at the monster can be seen bouncing off the sky backdrop.
Revealing mistakes: As the monster lumbers through Tokyo, the emergency officials are shown evacuating their office just before the building is wrecked by Gojira. After the office has been destroyed, a shot shows the monster's tail outside the wrecked building, and the wires holding up the tail are plainly visible.