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.
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.