The text below I have taken from a web site that always attacks the Qur'an: (Dr. Labib: You mean, in the Qur'an are there any mistakes and errors? I will tell you something. There are many errors in the Qur'an; many, many, many errors in the Qur'an. And I say that from a ten-feet viewpoint. For instance, when the Qur'an said that the earth was flat, that was a mistake. And again, when it talked about Mary, the mother of Jesus, you know what the Qur'an says? "You, sister of Aaron." You, sister of Aaron, Mary, the mother of Jesus is the sister of Aaron? How come? The difference between the Mary, the mother of Jesus, and Mary, the sister of Aaron, is 1,300 years! But you see, when you read in the Qur'an, it says about Mary, the mother of Jesus, "You, sister of Aaron.") I will be very happy if you comment about this text and if you have any answer for this Labib.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

The Quran is the words of Allaah, falsehood cannot approach it from before it or from behind it, and it is free from any modifications or alterations, and it is preserved from mistakes, and (safe) guarded from (tongue) slippers.

Allaah Says (what means): {Indeed, it is We who sent down the message [i.e. the Quran ] and indeed, We will be its guardian.}[Quran 15:9] Allaah also Says (what means): {Then do they not reflect upon the Quran ? If it had been from [any] other than Allaah, they would have found within it much contradiction.}[Quran 4:82] Therefore, it is imperative for every Muslim to believe that the Book of Allaah (the Quran) is safe from errors, mistakes, modifications and contradiction because it was revealed from Allaah, The All-Wise, The Well-Acquainted.

As regards the two questions which the person whom you mentioned in the question claimed that they are mistakes in the Quran, then the answer is as follows:

The first issue: Allaah has mentioned that the earth is flat which means: it is made smooth and docile (so as) to be stable and suitable for settlement, which does not reject that the earth is round-shaped. Imaam Al- Fakhr Ar-Raazi when interpreting the verse {And at the earth — how it is spread out.}[Quran 88:20], he said in his Tafseer (interpretation of the Quran): "(The earth) is straitened in a smooth, leveling (matter) to make it easy for the inhabitants to walk upon it. However, some people inferred from this that the earth is not round-shaped. However, this is a weak opinion because if the earth which is round-shaped is extremely huge, each part of it will be flat [as a flat (thing).”]

For more benefit, please refer to Fatwa 87767.

The second issue: The saying of Allaah (which means): {O sister of Aaron, your father was not a man of evil, nor was your mother unchaste.} [Quran 19:28] There are many (different) interpretations about this verse, such as Ibn Katheer's and others' interpretations:

The first interpretation: Aaron in this verse refers to the brother of Moosa (Moses) so the meaning is: "O you, (Maryam) who is like Aaron in worshipping Allaah" {...your father was not a man of evil, nor was your mother unchaste.}; which means: you are from a good, pure family that is known for their righteousness, worship and asceticism; so how did you do this? This is like the saying of Allaah about the spendthrifts (which means): {Indeed, the wasteful are brothers of the devils.} [Quran 17:27]

The second interpretation: Maryam is of the children of Aaron, the brother of Moosa, and she is ascribed as (his) sister because she is of his offspring; in the same way that (they) say for At-Tameemi (tribe): 'O you, brother of At-Tameem; and for the Arab (man): 'O you, brother of Arabs.'

The third interpretation: Maryam had a brother named Aaron who was pious and righteous, and he was loved by his relatives and this does not refer to Aaron, the brother of Moosa .

This last interpretation is proven by Ibn Katheer who mentioned in his Tafseer (interpretation) from Al-Mugheerah Ibn Shu'bah who said: "The Prophet sent me to Najraan, and they said: "Have you noticed what you are reciting {O sister of Aaron}, while Moosa was before 'Eesa (Jesus) [] for such and such a (time). He (Al-Mugheerah) said: "I came back and told this to the Prophet and he [the Prophet] said: "Why didn't you tell them that they used to name themselves after the previous Prophets and righteous people." However, this was only reported by  Muslim, At-Tirmithi and An-Nasaa'i .

In other words, this misconception was raised at the time of the Prophet and the latter answered it.

Hence, such a misconception and similar ones are propagated by the enemies of Allaah and the enemies of this religion;  Allaah Says (what means): {And they will continue to fight you until they turn you back from your religion if they are able.} [Quran 2:217]

Finally, it should be noted that you should stay away from viewing such sites on the internet as this is very  dangerous to your belief unless you have a strong faith and are very knowledgeable in religion so that you can answer their misconceptions and refute their ideas.

Allaah Knows best.