In the Qur'an we find the following statements about the moon and the stars:

He Who created the seven heavens, one above the other ...
And We have adorned the lowest heaven with lamps ... (67:3,5)

And He completed them seven heavens in two days
and inspired in each heaven its command;
and We adorned the lower heaven with lamps,
and rendered it guarded... (41:12)

We have indeed adorned the lower heaven with the beauty of the stars. (37:6)

Do you not see how God has created the seven heavens
one above the other,
and made the moon a light in their midst,
and made the sun as a lamp? (71:15-16)

The above is Yusuf Ali's translation. Pickthall renders Sura 71:16 as

And hath made the moon a light therein, and made the sun a lamp?

The Qur'an seems to teach that there are seven heavens, one above the other, whether it was imagined to be like storeys in a high building (flat layers) or like shells or the layers of an onion.

As a poetic way of expression this is acceptable, even though there are, scientifically speaking, no discernable stages in the universe that would allow us to differentiate between those various heavens.

However, the Qur'an specifically assigns the stars to a lower or even the lowest heaven, while it states the relationship of the moon to the totality of the seven heavens is that it is "in them" (fehinna). This gives the impression that the moon is at least as far away as the stars if not further.

But everyone knows today that the stars are much much further away from the earth than the moon. This is not a small difference, it is an issue of several magnitudes. The average distance from the earth to the moon is 384,400 km, while Proxima Centauri, the closest star to us outside of the solar system, is already about 4.3 light years = 40,682,300,000,000 km (40 trillion kilometers) away, or expressed differently, we need to multiply the distance of the moon by more than 100 million to reach even the nearest of all the stars.

Had the Qur'an formulated "and the moon in the middle of them" then this would have been unambiguously wrong. The formulation "in them" is vague enough to still allow the possibility of the moon to be in the lowest heaven as well. The wording of the Qur'an is certainly less than scientific in this instance and suggesting wrong notions even though it is sufficiently vague to not make it a clear error. It does, however, throw substantial doubt on the claim that God made the Qur'an scientifically as a proof of its divine origin.

Though it seems quite strenuous, one could say that maybe all the stars are in the lowest of the seven heavens (as the Qur'an does) and the moon is on the lowest part of the lowest heaven (which the Qur'an neither says nor implies). The Qur'anic expression relates the location of the moon to the plurality of the heavens and says that the moon is "in them". It does not say it is exactly in the middle, but it does say somewhere "inside" when we look how this word is used elsewhere.

There are a good number of other verses where the Qur'an uses the exact same Arabic word "Fihinna" as in the verse we are talking about. In the verses 9:36 and 2:197 it is used in the phrase "the holy months, IN THEM do not ...", i.e. with the meaning of "during this time". It is used speaking of a temporal "inside".

In the following a list of verses where this word is used for location:

55:56

(about the gardens of Paradise)
IN THEM will be (Maidens), chaste, restraining their glances, ...

55:70

IN THEM will be fair (Companions), good, beautiful;-

This is clearly stating that these beautiful women are inside these gardens, and more or less in the middle or distributed, but not that they are all huddling on the boundaries of it. This will be imporant below.

5:120

"Never said I to them aught except what Thou didst command me to say, to wit, 'worship God, my Lord and your Lord'; and I was a witness over them whilst I dwelt AMONGST THEM; when Thou didst take me up Thou wast the Watcher over them, and Thou art a witness to all things.

Again, this is about Jesus, and the whole point is that he lived AMONG THEM, not a life at an obscure point at the periphery, not he was in their midst and they have no excuse that they did not hear his message because they didn't know about it.

17:44

The seven heavens and the earth, and all beings THEREIN, declare His glory: there is not a thing but celebrates His praise; And yet ye understand not how they declare His glory! Verily He is Oft-Forbear, Most Forgiving!

Again, the totality is meant, not just the beings at the periphery.

23:71

If the Truth had been in accord with their desires, truly the heavens and the earth, and all beings THERIN would have been in confusion and corruption! Nay, We have sent them their admonition, but they turn away from their admonition.

Again, IN THEM, means 'inside' those living in the earth or in the heavens.

Finally the verse 71:16 that is in question:

Pickthall: And hath made the moon a light therein, and made the sun a lamp?

Yusuf Ali: And made the moon a light in their midst, and made the sun as a (Glorious) Lamp?

Clearly "in their midst" is a valid translation and there is no need to understand this as "exactly in the middle heaven" but it is "inside". What does "in" refer to? It is THEM, i.e. the seven heavens, since that is what the Qur'an talks about in the verse before it.

Do you not see how God has created the seven heavens
one above the other,
and made the moon a light in their midst,
and made the sun as a lamp? (71:15-16)

No indication that the moon is on the boundary of these heavens, or even at the lower boundary of the lowest one of the seven. The natural reading is still "somewhere inside". And clearly, Yusuf Ali thought that was the natural reading.

In distinction to this, we have the very clear statement that the stars are "on the boundary" of the seven heavens since they are in the LOWEST heaven as Sura 67:5 says.

As such, maybe one cannot say that the moon is further away than the stars, but given that the stars are in the lowest and the moon is inside the heavens, the moon is at least as far away as the nearest stars and that is scientifically problematic. If it is not outright wrong what the Qur'an says due to the vagueness of expression, it does nevertheless give a wrong impression.