In summary, this objection has (some) merit to it, and the common way of using "science in the Quran" or "scientific miracles" to provide evidence for Islam is faulty. In the same way, the anti-Islam arguments of scientific faults in the Quran are extremely faulty.
In this answer, I will explain why they are both faulty and an alternative way of proving that Islam is true with science if someone really wants to stick with science.
What are the proofs of Islam other than scientific?
Due to some factors like famous dawah personalities concentrating on them and due to the popular nature of science today, people think scientific arguments are the strongest (if not only) argument for Islam. This is far from the case.
I do not like the use of science to prove Islam for several reasons. Partly due to the faultiness of the actual arguments used (as will be shown) and partly due to the fact that science is ever-changing.
There are much clearer proofs of Islam. Among them are prophecies, miracles, the Quran and its challenge, and more. Some more resources: Collection of Articles & Videos and Short Video Playlist.
The proofs of Islam are many and evident, these scientific arguments are unneeded, and them being faulty is all the more reason to not concentrate much on them.
Common/Popular Formulation of Scientific Miracles
Quran says "ABC."
Modern science confirms "ABC."
It was not possible for the people of the 7th century to know "ABC" (or even guess it).
Hence, the Quran did not come from people. It came from God.
Repeat for a hundred different things.
On the surface, the logic is fine. It is based on the fact that Allah is all-Knowing and He can never be wrong, which is all well and true.
Indeed, Allah is Knower of the unseen [aspects] of the heavens and earth. Indeed, He is Knowing of that within the breasts. (35:38)
The issue is in the common execution.
Most of these scientific arguments fail in step 1 and/or step 2. The pitfall in step 1 is that the verses do not clearly say "ABC." There is a lot of twisting and turning. The pitfall in step 2 is that the science they are trying to associate with is not that confirmed.
To simplify this, I will call it the issue of vagueness (in the verses) and uncertainty (in the science).
Claimed Scientific Mistakes in the Quran
This is simply the mirror of the scientific argument:
Quran says "ABC."
Modern science confirms "ABC" is false.
Hence, the Quran is not from God.
Repeat for a hundred different things.
In this case, there is the same issue. The problem of vagueness and uncertainty applies to both most of the scientific miracles claimed and all the scientific mistakes claimed.
So, it is correct for an observer to say: How can you accept the vague and uncertain scientific miracles as evidence for Islam while you reject the claimed scientific mistakes of the same level of vagueness and uncertainty?
We cannot fairly do that. Either we stop using scientific miracles that are so vague and uncertain or we need to accept scientific mistakes of the same level as valid evidences against Islam.
We cannot use vagueness to reach the truth. As Allah says:
Indeed, assumption avails not against the truth at all. (10:36)
Science and the Quran
Before I explain what is a better way to use science to prove that Islam is true (although I don't recommend it be the main evidence), first one needs to understand what the exact relation is between science and the Quran.
Reality is true. The Quran is the word of God, so it must be true. If the Quran is true, it can never contradict reality. If something is truly reality, it cannot contradict the word of God.
Science is an interpretation or extrapolation based on reality. Likewise, tafsir is an interpretation or explanation of the Quran.
Some science can be strong, meaning it is so much supported by reality that it is highly likely to be true. Some science can be speculative. Some can be completely definite. Likewise with tafsir: some is strong, some is speculative, and some is definite.
What we can say is that definite science can never contradict definite tafsir of the Quran.
One of the evidences of Islam may be that no definite tafsir ever contradicts definite science.
Whenever there is a claimed contradiction, the issue is almost always that the claimant deceptively pushes one possible tafsir over other possible ones. Never is it a simple case of Quran saying "ABC" definitely and then definite science contradicting it.
The fact that disbelievers use vague verses to try to disprove Islam is even mentioned in the Quran itself:
It is He who has sent down to you, [O Muhammad], the Book; in it are verses [that are] precise - they are the foundation of the Book - and others unspecific. As for those in whose hearts is deviation [from truth], they will follow that of it which is unspecific, seeking discord and seeking an interpretation [suitable to them]. (3:7)
This approach has the advantage of dealing with this objection of Greek mythology. Greek mythology clearly says several things that contradict clear science.
So, this is the question left for non-Muslims to answer: how is it that the Quran consistently seems to only clearly state claims that are true? Any other book or mythology always has some claims which are clearly false.
Quran is Not a Science Textbook
You have probably heard the phrase several times before, but it is important to understand what it means. The Quran did not come to fix people's understandings about science. Don't misunderstand me however. Everything the Quran says is true, but it didn't come to teach people the exact understanding of science.
So, even if whatever the Quran says of how the universe works is always true, it does not mean people in the past can't misunderstand it or it can't fit into their understanding well.
A prime example is the fact that the Quran says the sun moves in a path. To some people in the past, it might seem like the Quran is saying the sun revolves around the earth. We know, of course, that this is not true. The sun does move but around the galaxy.
The Quran did not come to correct people's understandings from it revolving around the earth to it revolving around the galaxy. Rather, the purpose of the verse is to highlight Allah's control and schedule and it makes no difference if people understand it according to an incorrect scientific view. However, what the Quran says in essence (that the sun moves) is true.
And Allah knows best.