Qur'an 19:27-28--"At length she brought the (babe) to her people, carrying him (in her arms). They said: 'O Mary! Truly an amazing thing hast thou brought! O sister of Aaron! Thy father was not a man of evil, nor thy mother a woman unchaste!"
Notice that the Qur'an refers to Mary (the mother of Jesus) as the "sister of Aaron" (i.e. Miriam, the sister of Moses and Aaron). Even Christians during the time of Muhammad recognized this error, and Muhammad had a chance to respond.
Sahih Muslim 5326--"Mughira b. Shuba reported: When I came to Najran, they (the Christians of Najran) asked me: You read 'O sister of Harun ["Aaron"]' (i.e. Hadrat Maryam) in the Qur'an, whereas Moses was born much before Jesus. When I came back to Allah's Messenger (may peace be upon him) I asked him about that, whereupon he said: The (people of the old age) used to give names (to their persons) after the names of Apostles and pious persons who had gone before them."
So Muhammad's response is that people in the time of Mary would refer to a pious young woman as the "sister of X," where X might be a prophet from 1400 years earlier. The problem is that we have no record of such a practice in first century Israel, and we don't even find it used elsewhere in the Qur'an. The obvious conclusion, then, is that Muhammad simply made a mistake, and that he tried to correct it by making something up.
Two more points are worthy of note in al-Muslim's hadith. First, the Christians of Najran knew nothing of the practice of referring to pious young women as the sister of some prophet, even though they would have been familiar with traditions about Mary. Second, the Muslim who talked to them obviously didn't know that this was a figure of speech, since he was stumped by the refutation and had to go back to Muhammad for an answer. Thus, Christians knew nothing of the practice Muhammad referred to, and Muslims who had been reciting the Qur'an in Muhammad's presence were never told that "sister of Aaron" was a metaphor. Indeed, they only learned this when Muhammad had been accused of erring.
But things get even worse. The father of Moses, Aaron, and Miriam was a man named Amram (Arabic: "Imran"):
1 Chronicles 6:1-3--"The sons of Levi were Gershon, Kohath and Merari. The sons of Kohath were Amram, Izhar, Hebron and Uzziel. The children of Amram were Aaron, Moses and Miriam."
Hence, if Muhammad really believed that Mary the mother of Jesus was the same person as Miriam the sister of Moses and Aaron, it wouldn't surprise us to find Muhammad referring to Mary as "the daughter of Imran." Not surprisingly, this is exactly what we find in the Qur'an and the Hadith:
Qur'an 3:35-36--"Behold! When the wife of Imran said: 'O my Lord! I do dedicate unto Thee what is in my womb for Thy special service: So accept this of me: for Thou hearest and knowest all things.' When she was delivered, she said: 'O my Lord! Behold! I am delivered of a female child!'--And Allah knew best what she brought forth--'And no wise is the male like the female. I have named her Mary, and I commend her and her offspring to Thy protection from the Evil One, the Rejected.'"
Sahih al-Bukhari 3769--"Narrated Abu Musa Al-Ashari: Allah's Messenger said, 'Many amongst men attained perfection but amongst women none attained the perfection except Maryam (Mary), the daughter of Imran, and Asiya, the wife of Fir'aun (Pharaoh)."
Note that Mary's mother is called "the wife of Imran." The Qur'an certainly takes the application of this metaphor to an extreme, for now we must assume that there was a first century practice in which a pious woman would be called the "wife" of the father of a prophet!
Thus, if we are to believe Muhammad's explanation for what appears to be a rather obvious error in the Qur'an, we must believe that there was a first century practice in which people would refer to a pious young woman as "the sister of X" (where X was a prophet who died centuries earlier), and as the daughter of the wife of Y (where Y was the father of prophet X), and as "the daughter of Y" (where, again, Y was the father of prophet X). When we combine this with the fact that, by an amazing coincidence, there was indeed a woman named Miriam who was both the sister of Aaron and the daughter of Amram, and whose mother was the wife of Amram, we have to wonder why the author of the Qur'an would pass on such a confusing collection of metaphors, with absolutely no evidence that these metaphors were ever used in the first century, and with the only reasonable conclusion being that Muhammad didn't know that Mary and Miriam were two different people, who lived more than a thousand years apart.