Factual error: When the Marines strip off and run into the sea in the final scene, Doc takes off a pair of white socks that would be more appropriate for a final at Wimbledon. Not only are they white rather than khaki, they are virtually spotlessly clean which would be impossible after a week of fighting on the black sands of Iwo Jima.
Continuity mistake: When the "Flag-Raisers" begin stripping down to go swimming, they show a few of the Marines already down to their boxers. They switch to a shot of Bradley and then back to the Marines and all have their pants on.
Continuity mistake: When the marines start marching inland, where the Japanese are not shooting, you see several clips of the row of soldiers walking inland, then a clip of their waiting comrades, and then a clip of the soldiers - still walking in the exact same place, without moving forward.
Deliberate mistake: During the scene on the train in lounge car, a picture on the wall prominently shows an ALCO PA locomotive. The movie was set in 1945, but this locomotive was first produced in 1947.
Continuity mistake: When Ira exits the stadium after the flag show to vomit, the alleyway in which he vomits is at first dark. In the next few shots, it is lit up and then once again dark.
Other mistake: During the hill climb up terrain shaped like a valley with rocks on either side, a soldier is directly hit with a large explosive, probably from the big guns, and his severed head lands down on another soldier's back, who is crouching to help another man. When the head lands on his back, it is just an empty helmet, but when he looks at it on the ground, you see the partially alive, severed head lying next to it with much of the neck still attached.
Factual error: The water is perfectly still around the ships as they bombard the island. When the cannons fires there are small ripples on the water from the shockwave, but around the ship it remains perfectly calm.