Are there grammar mistakes in the Quran?

Some time ago I read a post by an infamous Christian whose name I will not mention, which claimed that the Quran had grammatical mistakes. There is a short book on this topic that lists the mistakes and gives the corrections. In simple words the way they put it, the Quran’s author did not know Arabic. As I mentioned before we will write the simplest yet most effective and concise rebuttals.
I would like every reader who studied any language to think about grammar and linguistics. The ones that never studied a different language can use their rational and intellect that God gave them. Are you ready? Which comes first the speaking of the language or the writing of it? Which comes first, the spoken language or grammar? Did the old Arabs have grammar class? Some of them did not even know how to read and write yet they were the most proficient in the language. Grammar is a set of rules that breaks down the language and analyzes it in order for those who do not speak it to learn it. It is not the other way around. Grammar did not come first; it was the language that came first. Therefore all the alleged mistakes are actually lack of knowledge of the Arabic from the accusers. The Arabic that most people speak today is washed out into slang and so is most of the grammar. We need the grammar lessons in order to go back to the original language that was spoken by the people who had the organic Arabic in the first place. An example should clarify my point: Shakespearean English is so different than American English. I remember the first time I heard it I thought that Shakespeare did not know how to speak English. The truth is his English was the closer to the original English and without a doubt he did not have to explain to people the past tense, the active and passive speaker, nouns and so on. They all understood his language and they all praised his compositions.
The truth is that there are not grammatical mistakes in the Quran. The Quran is the highest authority in the Arabic language, and keeping in mind rhetoric of the Fusha (Quran Arabic Eloquence), the people who accuse the Quran of having mistakes are the ones who should attend some Arabic grammar classes.