If you need something that is actually controversial about the Battle of Iwo Jima, the best place to look is at the issue of whether the battle was actually necessary and helpful for the American cause.
The Battle of Iwo Jima was terribly bloody. The Japanese were dug into a maze of tunnels in the island and managed to hold out for more than a month even though the island was very tiny. The Marines who landed on Iwo Jima needed to kill practically all of the Japanese soldiers since they were unwilling to surrender. This meant that large numbers of Americans were killed or wounded in the battle. Almost 7,000 Marines were killed and 20,000 wounded. This was a huge number for a battle over such a small amount of land.
The issue, then, is whether the battle was worth it. The usual argument given is that the US needed this island as a place for emergency landings by B-29s bombing Japan from bases in the Marianas. However, some people (as in the historynet.com link below) believe that the island was never really instrumental in saving the lives of many airmen. Therefore, the argument goes, it would have been possible to bypass Iwo Jima without any serious harm to American interests. The US could simply have gone on to invade Okinawa without taking 27,000 casualties on Iwo Jima. The Japanese on Iwo Jima could have been left to “wither on the vine” like the garrisons had been in places like Truk and Rota.
So, the major argument about this battle has to do with whether it did enough good to warrant the number of casualties that the US incurred.