One of the claims does interest me as a biologist, and also as an atheist who gets this ploy used on me a lot. This is the claim that the qur'an anticipates modern (human) embryology. This could only have a divine origin (despite its erstwhile similarities to Galen, for whom no such divine inspiration is attributed).
The relevant verses are 23:12-14. So I just want to look at these quickly.
We created man from an extract of clay. Then We made him as a drop in a place of settlement, firmly fixed. Then We made the drop into an alaqah (leech, suspended thing, and blood clot), then We made the alaqah into a mudghah (chewed-like substance)...
[Noble Quran 23:12-14]
Clay23:12 claims that humans are made from clay. Now because clay is mostly aluminum and silicon and contain little of the organic material this is clearly not the case (the 6 macro-elements we look for as life's basic building blocks are Hydrogen, Oxygen, Nitrogen, Phosphorus, Carbon and Sulphur). It is perhaps more likely this is meant in an allegorical rather than scientific sense. But if we accept this is not being scientific, then well, it is not clear why the remaining verses are supposed to be scientific.
Nutfah23:13 introduces the drop (nutfah) which also presents problems. It doesn't take divine inspiration to realise that the ejaculate from a male can be a liquid drop. It would be impressive if the qur'an mentioned sperm and eggs. But it doesn't. In fact, eggs (baydeh) are nowhere mentioned. It strikes me that as a guide to modern embryology, omitting any mention of eggs is well, astonishing. Parenthetically, sperm isn't mentioned either. Sometimes special pleading is used to infer that the nutfah means a human gamete. But there is nothing here that hints at the microscopic world.
The claim of a safe lodging would also contradict ectopic pregnancies, where the gamete might settle in the fallopian tube or abdomen. This unsafe location causes miscarriages or at worst, painful pregnancies fatal to mother and child.
Alqahah23:14 then gets very complicated as many words gets vaguer. The first stages of embryology (blastula, gastrula) don't involve any blood vessels, so a clot isn't a good description. It seems more plausible that the spotting that sometimes occurs in early pregnancies- or even miscarriages- would cause a 'blood clot' deduction.
Alternatively, alaqah could be a metaphor based on a leech. If so, it is not a very good one. Leeches are protostomes whilst humans are deuterostomes. We haven't been alike for about 600my. Leeches lack a notochord, they lack limb buds, they lack pharyngeal arches. A human embryo doesn't digest its host's blood. It doesn't use its mouth-parts to interact with its host.
Even if we want to go with a leech-like interpretation over the blood-clot for alaqah, then this does not imply divine insight. For a people familiar with butchering animals (and dare I say, people on occasion), it wouldn't take much powers of observation to notice small embryos attached to the uterus of pregnant mammals. For ancient peoples, these likely resembled leeches.
BonesThe text above omits the last part of 23:14. Here are two translations of it:
The issue here is simply the order bones appear. It appears to describe two stages. First, the mudghah becomes bones, then the bones are covered in flesh. This is likely a deduction of people used to butchering animals, and had no way of conceiving how muscles and flesh could be attached to bones without the skeleton being formed first.
Muhsin Khan Then We made the Nutfah into a clot (a piece of thick coagulated blood), then We made the clot into a little lump of flesh, then We made out of that little lump of flesh bones, then We clothed the bones with flesh, and then We brought it forth as another creation. So blessed be Allah, the Best of creators.
Pickthall Then fashioned We the drop a clot, then fashioned We the clot a little lump, then fashioned We the little lump bones, then clothed the bones with flesh, and then produced it as another creation. So blessed be Allah, the Best of creators!
The problem is that bones form last. Reduced to the basic steps, mesenchymal cells within the embryo first differentiate into cartilage lines. Later this cartilage is replaced by bone. At no point would we say that the bones are later covered in flesh.