Quran: Is it really Impossibe for people to create a book without discrepancy?

Do they not consider the Qur'an (with care)? Had it been from other Than God, they would surely have found therein Much discrepancy.
(4:82)

I think this statement is wrong.  Think about that! The statement in the Quran that claims that a lack of discrpancy is a proof that it is from God, that is itself an error!
There are surely many novels, technical documents and mathematics books that do not contain any discrepancies. Even if errors were found, you could keep fixing them until there were none left.

Apart from the fact that this challenge is inherently wrong, I would like to point out that it does not make sense to make a challenge like this.

Let me give a specific example:
So believe in Allah and His messengers, and say not "Three" - Cease! (it is) better for you!
(4:171 Pickthall)

Note you cannot recite this verse without saying "Three".  People who recite the Quran violate the Quran all the time.

Muslims will find a justification for this, but you can will regard this as a contradiction.  Who is to judge whether the Muslim justification can overcome what you regard as a contradiction?  As the verse is evidently written for the benefit of unbelievers, that would make you the judge.

Also, the Quran has a built-in system for abrogating verses.  I may discuss this elsewhere.

The Quran is written by just one person over a short time, not by many people over thousands of years.  Consider how in a sermon you will routinely hear a verse from one end of the Bible and the speaker jumps to the there end of the Bible with no perception that there are thousands of years between the two.

I was once told that when you buy an oriental hand-made carpet made Middle-eastern carpet made by Muslims, that carpet  there always have a deliberate mistake put in somewhere because nothing is perfect but the Quran.

There is no equivalent challenge that is articulated in the Bible.  Our faith is based on the resurrection.