Now the serious post:
Of what you listed, there is absolutely nothing to fix.
Concerning the helmet you call a dunce cap, it's the Pylos helmet adopted en masse by the Spartans sometime around the end of the 5th century B.C. (So 200 years before the mod) and quite common in Greece after it (And yes, the Spartans used that particular helmet during the battle of the Thermopylae, the movie is mostly fiction). Call it silly but it was an affordable helmet for the poorer classes, easy to produce and it didn't restrain hearing and visibility unlike the Corinthian helmet which entered in decline in favor of the new helmet "trends" such as the pylos, boeotian, phrygian, thracian and attic families of helmets.
You can read a short resume here (I bet you won't and just thrown some weightless arguments against our choice but here is anyway):
http://www.mediafire.com/view/66jbt73zlwcw061/Helmets-libre.pdf
Apart from a certain form of Thracian helmet, some old fashioned attic or chalkidian helmets, nose bridges are practically non existant during this period.
Regarding the troops, the states rarely if ever provided any equipment for the peasants, it was mostly your task to manage to gather some equipment before being sent to war. Athens for example provided a spear and a shield to the recruits and the full panoply was only awarded to a small force of elite soldiers, known as the Epilektoi (picked troops). Lower classes would fill the light infantry and skirmisher roles, middles classes would fill the bulk of the army and upper middle class and nobles would fill the cavalry ranks if they could afford a horse, certain states like Sparta that tried to maintain a cavalry force would pay from its pocket but in that particular case they weren't so eager to fight mounted and most often the mounts were bought on the eve of a campaign which isn't great to build a horse-horseman bond nor train both for war the rest of the nobles and whoever could afford would fill specialized forces such as bodyguards, heavy cavalry, heavy infantry, etc... And the rest would cut off their thumbs because they feel it beats being slaughtered on a battlefield.
In short, a peasant is a peasant, a noble is a noble and at that time social classes matter for most of the civilizations. Don't try to mix them all.
