Two verses of Sūrah Yūsuf read:

The brethren sold him for a miserable price, for a few Dirhams counted out: In such low estimation did they hold him! (12:20)

...As for the other, he will hang from the cross, and the birds will eat from off his head... (12:41)

Now Dirhams, from Greek, ‘drachma’ the small silver coins, were not in use at the time of Joseph’s story related in Sūrah Yūsuf, namely about 1700 BC. They were first used as standard coins in the ancient Greek empire about 600 BC or even later!

12:41 given above speaks about one of Joseph’s prison inmates who would be killed by being crucified, hanging on a cross. Historically, however, the capital punishment of crucifixion was only invented and used during the Roman empire starting from about 500 BC!

Now my question is: How is it possible that the Qur’ān contradicts historical facts?

Answers: As for the first verse, in my opinion, the Qur’ān has used the name of the most commonly used coins in vogue during the time it was being revealed to merely connote coins of a earlier era. In other words, the word Dirham is used in the verse to merely mean coins. Such usage is common in many languages. Let me give you an example of such usage from the English language: If I say ‘I don’t have a penny’, I actually mean that I don’t have any money. Here I am not negating the existence of a penny. I am negating the mere existence of money. So the correct translation of the verse, in my opinion, is

They sold him for a meager amount of a few Dirhams. (12:20)

As far as your second observation is concerned, it needs to be appreciated that the Arabic word Taslīb (to crucify) means to nail somebody on ANY form of framework to punish him. This framework can be a cross, a tree, a wall -- anything which can bear the weight of a human body. Thus we find in the Qur’ān the Pharaoh telling his magicians that he will crucify them on a tree stem as a punishment for professing faith in Moses (sws):

I will cut off your hands and feet on alternate sides and crucify you on the trunks of palm trees. (20:71)

In other words, crucifixion on the cross for capital punishment may have been invented during the Roman Empire, but it seems that crucifixion on other structures was in vogue much before this period.