The world map seen in the Japanese command center on Iwo Jima does not demarcate the then British colony of Newfoundland, including it a part of Canada instead. Newfoundland did not join Canada until 1949.
In the scene where General Kuribayashi recognizes Saigo in the tunnels, his clearly visible tunic collar insignia are that of a Chujo (Lieutenant- General), consisting on two silver five-pointed stars over a yellow strip. Instead Kuribayashy was promoted to full generalship (Japanese rank Taisho) in March 1945 before being sent to Iwo Jima, and he should wear a yellow collar strip with three silver stars.
The Japanese script uses a number of "gairago" (foreign loanwords), which are in current use, but would have been frowned upon by the nationalist government at the time. These include "raifuru" for "rifle" and "jiipu" for "jeep".
During the rainstorm about 25 minutes into the movie, several soldiers disembark from a plane. The first soldier's clothing is nice and dry before he steps out into the rain but the second two already have wet jackets, suggesting this was not the first take of this scene.
In the second-to-last scene, the captured Japanese soldier is taken to the American landing zones, which were exclusively on the east of Iwo Jima, just north of Mt. Suribachi. The soldier, Saigo, then witnesses the sun 'setting' in the east, not the west.
It is mentioned a few times that Admiral Ozawa's fleet was utterly destroyed off the Marianas. This is incorrect. While it is true the Japanese naval air forces were wiped out, the US Navy only sank 3 carriers. The remainder of the IJN fleet remained intact and was quite powerful consisting of more than 10 battleships and other heavy ships. The IJN was not fully destroyed until the US invaded the Philipines in Nov. 1944.
The artillery shell landing near Saigo when he empties the stinky bucket does not exhibit rifling marks on its driving band. Any shell fired through a rifled barrel would show these, therefore this projectile had never been fired from a gun.
The goof item below may give away important plot points.
In the tunnel battle to defend Mt Suribachi, when the Japanese soldier looks up the cave opening and is about to get set alight by the Marine's flamethrower, it is clearly visible that the uniform has been wetted with the fireproof grease, but a few moments before that, his uniform was completely dry.