While most of the Spartans wear the correct headgear, Leonidas and his officers wear Roman legionnaire style helmets that wouldn't be around for about 200 years. (This may have been so that they could easily be identified.)
When the Persian army is into Greece where they will meet the Spartans, they are marching between mountains on their left, and water on their right. In actuality, the Persians were marching south along the eastern edge of Greece, so the water would have been on their left with mountains on their right. The way the movie portrays it, the Persians are marching out of Greece.
When the Spartan soldiers are in the water in that scene, "Night Attack", the ocean and the lower parts of the hills that are in the background are dark because its obviously "night". But in the background the daylight can clearly be seen. The lower half of the land is dark and the top half is illuminated. It's not the shadow of cloud, it's not supposed to be because it's night.
A character is clearly heard saying that the other army "runs like a machine." How would they know how a machine runs before the term machine has been commonly used? Greeks actually were familiar with the concept of machines in their plays. Plots would be resolved by a god being lowered or raised to the stage by machine, referred to in Latin as a "Deus ex machina"
When the Immortals attack, the javelins thrown by the Greeks have no points. Many of the Immortals can be seen dropping their weapons to grab the javelins and hold them under their arms or to their chests. A javelin with a blunt end can also be plainly seen hitting one of the extras in the mouth.
During the battle with the immortals, one of the Spartan "officers" is revealed to have a pink towel between his forearm and the shield itself to comfort and protect the forearm. This is revealed a couple of times during the battles.