I see that Iran's women's hair is visible from under their headscarves. Is it allowed by Shia fiqh? Is it denied by Sunni mazhabs?
As Nadeedm wrote, Shias agree that women must cover all their body parts except hands and face (provided they don't have make-up) but for some reasons Iran has failed to enforce this law uniformly on its citizens and Shia scholars seldom approve of harsh enforcement of Islamic code of conduct as they think it is counterproductive if not impossible. However it is misleading to evaluate popularity of ideal hijab in Iran by looking at the women in the streets especially those of Tehran. For Hijabi women less frequently show up in shops and their social activities are more inward and self-effacing. A recent poll in Iran showed that about 45 percent of Iranian women prefer Chador (The black veil) as their favorite Hijab including those who wear it casually.
Muslim women must wear the full veil curtain for all body when they are outside her home (in Public) or attend a foreign man,
As stated in the Qur'an:
And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their headcovers over their chests and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed. [24:31]
Thus, girls who reported they committed a sin, they must cover all the hair and deprives them from showing any part of it when going out or in absence of any foreigner.
And this provision agreed in Sunnah and Shia.
To the best of my knowledge, both Shia and Sunni order to cover all of the hairs of the head.
In regards to what you gave an example about Iran, I can explain that:
Shia Fiqh (jurisprudence) considers it haram even if a part of women's hair is visible. On the other hand, all of women are not so in Iran, and many of them (especially in more religious cities) cover all of their hairs.
If a number of women don't cover all of their hairs in Iran, that's related to their (personal) incomplete obedience in regards to this Islamic order ..., and actually it is not related to the Fiqh of Shia Islam.
Meanwhile, I assume it is not true to judge so by seeing people of everywhere..., otherwise for instance it can be seen in most Sunni countries that (almost) majority of women don't cover their hairs, but it is not related to the rules of their fiqh but it can be related to the degree of their observing in Islamic issues.
In both Shia and Sunni figh, women must cover all of their heads' hairs.