Breaking the Fast Before Sunset in Uncertainty (Hadith No. 1675)

Question: if a person breaks their fast before sunset thinking that it was time for iftaar, do they have to make up for that fast?
A simple and straight-forward answer is "no", provided it wasn't intentional. For details and proofs, read on.
Volume 3, Book 31, Number 180:
Narrated Abu Usama from Hisham bin 'Ursa from Fatima:
Asma bint Abi Bakr (radiallaahu `anhaa) said, "We broke our fast during the lifetime of the Prophet (sallallaahu `alayhi wasallam) on a cloudy day and then the sun appeared." Hisham was asked, "Were they ordered to fast in lieu of that day?" He replied, "It had to be made up for." Ma'mar said, "I heard Hisham saying, "I don't know whether they fasted in lieu of that day or not."
Shaykh al-Islam Ibn Taymiyah said: 
Those who say that the fast is not broken if a person makes a mistake or forgets at the beginning or end of the day said: our evidence is stronger, and the evidence of the Qur’aan and Sunnah concerning what we say is clearer. Allaah says (interpretation of the meaning):
“Our Lord! Punish us not if we forget or fall into error”
[al-Baqarah 2:286]
Forgetting and falling into error are mentioned together, because the one who does things that are forbidden in Hajj or prayer by mistake is like one who does them out of forgetfulness. It was proven in al-Saheeh that one day at the time of the Prophet (peace and blessings of Allaah be upon him) they broke the fast and then the sun appeared, but it does not say in the hadeeth that they were ordered to make up that fast. But Hishaam ibn ‘Urwah said: It must be made up, but his father was more knowledgeable than him and he said, They do not have to make it up. And it was proven in al-Saheehayn that a group of Sahaabah used to eat until one of them could distinguish the white thread from the black. The Prophet (peace and blessings of Allaah be upon him) said to one of them, “Your pillow is wide [if the white thread (of dawn) and the black thread (of the night) are underneath your pillow], rather that is the whiteness of the day and the blackness of the night.” But it is not narrated that he told them to make up their fasts; they were ignorant of the ruling so they were making a mistake. And it is proven that ‘Umar ibn al-Khattaab broke his fast then it became clear that it was still day, but he said, “We will not make it up because we did not deliberately commit sin.” And it was narrated that ‘Umar said: “We will make it up,” but the isnaad of the first report is stronger. And it was narrated from him that he said, “It is not a serious matter.” So some of the scholars understood this as meaning that it is not essential to make it up, but the wording does not indicate that. 
In conclusion, this view is stronger in terms of reports and reasoning, and  is more strongly supported by evidence from the Qur’aan and Sunnah and analogy (qiyaas). 
Majmoo’ al-Fataawa, 20/572, 573
[Taken from IslamQA]