Historical Errors in the Quran
One of the major criticisms brought to bear against the Quran, as well as the Hadith, by both serious scholars and critics is that it reinforces historical misconceptions common among the Arab contemporaries of its 7th century author. While much effort has been exerted by modern Islamic scholars towards reconciling what appear to modern readers as blatant historical errors with the Islamic belief in the inerrancy of the Quran, their arguments have not yet won any assent outside their circles and are generally regarded as lacking rigor. It is important to note that modern Islamic scholars are not the first to note the contradictions between historical statements found in the Quran and the views of contemporary historians — in fact, even some classical Islamic scholars noted that there were certain historical claims in the Quran and hadith which, taken literally (as Islamic orthodoxy holds they should be), could not easily be reconciled with what they held to be basic and incontrovertible facts about history.
Regarding ancient religious doctrine
Mary as part of the Trinity
Mainstream Christian doctrine has never held Mary to be a part of the Trinity. The Qur'an, however, plainly states as much, leading some to conclude that Muhammad misunderstood Christian doctrine.
This alternative formulation of the trinity is present even more clearly in Quran 5:72-75, which makes no mention of the holy spirit and takes measure to disprove the divinity of Jesus and his mother by pointing out that they, like normal human beings, also ate food.
Regarding ancient religious doctrine
Mary as Miriam
Mary the mother of Jesus was born in the first century BCE and was not related to Moses and his family whose story is set 1500 years earlier. Miriam was the sister of Moses and Aaron and daughter of Amram (Imran). The Quran appears to confuse these two characters, as it describes Mary, the mother of Jesus, as the "Sister of Aaron" and her mother as the "wife of Imran" in context where the "Imran" being discussed is evidently Miriam's father. A possible source of this confusion is the fact that both Miriam and Mary had the same name in Arabic, or were at least similar enough sounding for the original distinction to have been lost or neglected (the word used in either case in the Quran is the same and is pronounced maryam).
Ezra as the son of God in Jewish doctrine
Historically, Judaism has been a strict form of monotheism. The Quran, by contrast, describes the Jews as practitioners of polytheism by stating that they hold Uzair (Ezra) to be the son of God. This is compared directly with the Christian doctrine which hold Jesus to be the son of God. This appears to be a confusion resulting from conflating the alternative senses in which Jewish and Christian theologians have employed and understood the word "son".
Regarding general history
Massive wall of iron
The Qur'an presents a version of the Syrian legend of Alexander the Great as a great king who helps a tribe of people build a massive wall of iron between two mountains. The Quran then states, along with the hadith, that this wall and the tribes it traps will remain in place until the Day of Judgement. Modern satellites and near comprehensive exploration of the Earth's surface, however, have yet to reveal any trace of such massive structure.
"Bring me blocks of iron." At length, when he had filled up the space between the two steep mountain-sides, He said, "Blow (with your bellows)" Then, when he had made it (red) as fire, he said: "Bring me, that I may pour over it, molten lead." Thus were they made powerless to scale it or to dig through it.
David invented coats of mail
Historians commonly credited the invention of coat mail (not to be confused with scale armor) to the Celts in the 3rd century BCE.. Mail has also been found in a 5th century BCE Scythian grave, and there is a cumbersome Etruscan pattern mail artifact from the 4th century BCE. The nature of coat mail is such that it should persist for several millennia, and such advantageous military technologies would spread rapidly, so it is unlikely that coat mail would have originated much earlier, undiscovered by archaeologists. While, older translations of the Bible mention Goliath and David wearing a "coat of mail" in 1 Samuel 17:5 and 17:38 respectively, this is a well known mistranslation for a word meaning armor in general.
In the Qur'an, by contrast, David in the 10th century BCE is taught by Allah how to make coats of iron chainmail (sabighatin سَٰبِغَٰتٍ) and to measure the chainmail links (as-sardi ٱلسَّرْدِ) thereof. Another passage adds that people should be thankful for this knowledge which has since passed down from David.
Crucifixions in ancient Egypt
The first historical reference to crucifixion as a method of execution is from 500 BCE, when the technique began being used in several middle eastern cultures. The Qur'an, by contrast, tells of crucifixions at the time of Moses (approximately 1500 BCE) as well as Joseph (approximately 2000 BCE).
Ancient Egypt has been subjected to extensive study by archaeologists. While there exists hieroglyphic evidence of people impaled through upright stakes in ancient Egypt, this remains distinct from the Palm-tree crucifixions described in the Quran, as Palm trees are of too great girth to be used to vertically impale an individual.
Samaritans in ancient Egypt
The Qu'ran states that Moses dealt with a Samaritan during his time, however the Samaritans did not exist until well over half a millennium after Moses is supposed to have existed. The term samari itself comes from the city of Samaria, an archaeologically evidenced city built by King Omri around 870BC, nearly 700 years after Moses is supposed to have existed.
The likely source of this confusion is the story in the Bible in Hosea 8:5-6 where there is mentioned another golden calf worshipped by Samaritans after the time of Solomon. One modern perspective holds that the Qur'an might be referring to Zimri, son of Salu (Numbers 25:14). However, the Quranic character is referred to three times in Quran 20:85-88 as l-sāmiriyu with the definite article, "the Samiri", so this is a descriptive title rather than a proper name.
The singular Pharaoh
Geographically, the Coptic land of Egypt is adjacent to Arabia. Thus, most Arabs were aware of the preservation method applied by the ancient Egyptian to their pharaohs. Pharaohs were preserved intact using methods such as salt to dry the body (hence, salt in the body of Ramesses II does not suggest that he drowned in the dead sea). There were many pharaohs from numerous dynasties who were preserved in this way. The Qur'an, by contrast, only speaks of "Pharaoh" (Firaun) singularly, as a proper noun without the definite article, suggesting that its author was unaware of the multiplicity of pharaohs.
Noah's worldwide flood
The Quran contains a version of the worldwide-flood story widespread in ancient near-Eastern mythology and most famously found in the Bible. Since geological evidence suggests such a flood never took place, some modern Muslim scholars have reinterpreted the account in the Quran as referring to a more limited, local flood. Several elements in the tale, however, militate against this rereading. Elsewhere in the Quran whenever the heavens and earth are mentioned together, it means in their entirety. In this story waters are released from both of them. Another such detail is the storage of "two of each kind" of animal aboard the ship, since it is not clear what purpose this would serve if the flood were local. Similarly, the purpose of the boat itself appears unclear in this reading - as with the ample warning time that Noah was given, he and his family could have simply evacuated the area that was to be flooded. The relevant passage also states plainly that nothing, not even a tall mountain, could save an individual from drowning on that day except for Allah - this seems to contradict the idea that individuals and animals could have escaped the flood simply by evacuating the flooded area. Noah is recorded praying to God, "O my Lord! Leave not of the Unbelievers [kuffar], a single one on Earth!" - the flood is an answer to this prayer, which likewise suggests that the flood described is a global flood that drowns all those not chosen by Allah to persist aboard the ark.
Flood waters boiled from an oven
The Qur'an further describes the flood waters as boiling from an oven. There is no scientific nor historical evidence for a large flood of this nature. This element is not found even in more ancient versions of the story (Epic of Gilgamesh, Atra hasis, and Ziusudra). Its ultimate origin appears to be a highly tenuous rabbinical exergisis in the Babylonian Talmud, based on a word in an unrelated verse that means heat or wrath.
Note that in his translation, Yusuf Ali mistranslates the Aramaic loan word for the oven (alttannooru ٱلتَّنُّورُ) as "fountains". The Arabic verb translated "gushed forth" (fara فَارَ) means "boiled" in the context of water in a cooking pot, as well as in the other verse where it is used, Quran 67:7.
Noah's ark holding every species
Part of the legend of Noah's Ark is that a pair of every living species was stored on board. Modern science has revealed, however, that there are over a hundred thousand species of animals including penguins, polar bears, koala bears, and kangaroos that live spread across the entire planet and each of which require different climates, habitats, and diets. These discoveries appear to render the idea that all animals could have been kept on board a single ship impossible.
John the Baptist's original name
The name "John" comes from the Hebrew name Yohanan. Several figures in the Old Testament bore this name. The name has also appeared throughout history. There existed a high priest named Johanan in the 3rd century BCE and a ruler named John Hyrcanus who died in 104 BC. These people existed before John the Baptist, who was a contemporary of Jesus. The Qur'an, by contrast, asserts that nobody before John the Baptist (Yahya in Arabic) bore his name.
Supernatural destruction of cities
The Quran state that outside the vicinity of Arabia there existed cities and tribes destroyed by Allah for rejecting his messengers and Islam. In each specific example presented in the Qur'an (the people of A'ad, Thamud, Midian, Lut (Lot), and the Pharoah's army), the destruction of the disbelievers is sudden and total. Archeological research, by contrast, has revealed that historical cities and tribes were only gradually ruined by natural disasters, famine, wars, migration, or neglect, often taking years or decades to unfold. In this respect, the Quran appears to have adopted and adapted contemporary Arabian myths regarding the destruction of neighboring cities, some of which may not have existed.
In the Qur'an, the people of Thamud are killed instantly by an earthquake Quran 7:78 or thunderous blast Quran 11:67, Quran 41:13-17, Quran 51:44, Quran 69:5. The people of A'ad are killed by a fierce wind that blew for 7 days Quran 41:13-16,Quran 46:24-35,Quran 51:41, Quran 69:6-7. The people of Midian (Midyan) are killed overnight by an earthquake Quran 7:91, Quran 29:36. The towns of Lot (Lut) are destroyed by a storm of stones from the sky Quran 54:32, Quran 29:34. The actual locations of these towns or tribes is unknown. Midian in particular was a wide geographical desert region rather than a particular location or city, which makes archeological investigation difficult.
Critics have also asked why it is that various other polytheistic cultures worldwide dis not encounter similar fates as those outlined in the Quran.
The suddenness of Allah's punishment is stressed repeatedly in Surah al-A'raf:
Humans lived for hundreds of years
The oldest verified human life was a little over 120 years. Based on fossil records and testing on human remains, anthropologists have concluded that human life spans are increasing rather than decreasing in both the long- and short- run. By contrast, the Qur'an states that Noah lived for almost 1,000 years. The idea of humans living for hundreds of years in the past is accompanied by the many hadiths, including accounts in Sahih Bukhari, which describe Adam as being 90 feet tall. The general doctrine appears to be that ancient humans were both gigantic as well as long-living.
Ancient Mosque in Jerusalem
Muslim scholars maintain that a long extant, ancient mosque was present in Jerusalem during Muhammad's life time. Historical research has, however, found this not to be the case.