I have a very simple but profound and important question:
How do we know the Quran is being interpreted correctly? The Quran is the word of Allah (a perfect entity) and is read by humans (not by any means perfect). How do we know that the Quran has been interpreted correctly by Muslims ('normal' Muslims, Imams, Caliphs, etc.). To me it seems unlikely that humans can possibly understand the exact thing Allah means, and this leaves a lot open for interpretation.
The simple answer is, you don't. Only God knows the true interpretation of the Qur'an:
It is He who has sent down to you the Book; in it are verses precise - they are the foundation of the Book - and others unspecific. As for those in whose hearts is deviation , they will follow that of it which is unspecific, seeking discord and seeking an interpretation. And no one knows its interpretation except Allah. But those firm in knowledge say, "We believe in it. All is from our Lord." And no one will be reminded except those of understanding.
[Aal-Imran 7]
All the scholars and books of tafsir — even the Qur'an itself — are merely means to an end; after a point, even those mufassir who have dedicated their lives to studying the Qur'an and its meanings still need to resort to conjecture.
So those who believe in Allah and hold fast to Him - He will admit them to mercy from Himself and bounty and guide them to Himself on a straight path.
[An-Nisa 175]
Regardless of which interpretations you read, or which scholars you follow, never forget that faith in God is the firmest handhold. Ultimately it is He who guides anyone to the truth, not human effort.
Very good question!
You have to read it yourself and understand it according to your true heart ( not to interpret in a way that you sincerely know you are altering the message )
There are clear verses which don't need any tafsir and they are the important of the divine message, the others needs effort ( believe me, sometimes a huge effort ) because you have to dig in several knowledges like epistimology, linguistics, history, Arabic syntax, logic, etc.
In this case, believing the veracity of the quran in the whole is what you will be questioned about - والله أعلم - if you cannot or have not the ability to try to understand the message :
هُوَ الَّذِي أَنزَلَ عَلَيْكَ الْكِتَابَ مِنْهُ آيَاتٌ مُّحْكَمَاتٌ هُنَّ أُمُّ الْكِتَابِ وَأُخَرُ مُتَشَابِهَاتٌ ۖ فَأَمَّا الَّذِينَ فِي قُلُوبِهِمْ زَيْغٌ فَيَتَّبِعُونَ مَا تَشَابَهَ مِنْهُ ابْتِغَاءَ الْفِتْنَةِ وَابْتِغَاءَ تَأْوِيلِهِ ۗ وَمَا يَعْلَمُ تَأْوِيلَهُ إِلَّا اللَّهُ ۗ وَالرَّاسِخُونَ فِي الْعِلْمِ يَقُولُونَ آمَنَّا بِهِ كُلٌّ مِّنْ عِندِ رَبِّنَا ۗ وَمَا يَذَّكَّرُ إِلَّا أُولُو الْأَلْبَابِ
The Quran is valid for every epoch, every generation have to understand it according to their level of knowledge.
Being stuck in the traditional tafassir is what put the muslim mind now in several troubles.
Hope this helps.
Regarding that you said "To me it seems unlikely that humans can possibly understand the exact thing Allah means" then why Allah the Wise ever reveal such an scripture? A scripture that is not going to be fully understood? You are right in that everyone are not able to understand it:
إِنَّهُ لَقُرْآنٌ كَرِيمٌ \ فِي كِتَابٍ مَّكْنُونٍ \ لَّا يَمَسُّهُ إِلَّا الْمُطَهَّرُونَ \ تَنزِيلٌ مِّن رَّبِّ الْعَالَمِينَ \ أَفَبِهَـٰذَا الْحَدِيثِ أَنتُم مُّدْهِنُونَ \ وَتَجْعَلُونَ رِزْقَكُمْ أَنَّكُمْ تُكَذِّبُونَ
That this is indeed a qur'an Most Generous [that is, open handed], / In Book well-guarded [that is, highly encrypted], / Which none shall touch but those who are clean [touching its face allowed only by having Vozu', and touching its deeper truth only by having clener hearths] / A Revelation from the Lord of the Worlds. / Is it such a Message that ye would hold in light esteem? / And have ye made only this your livelihood that ye should declare it false? [while you could exploit its messages many times more by accepting them!] [56:77-82]
And Ahlul Bayt --peace be upon them-- are the most purified and clean people after the holy prophet --peace be upon him and his household-- according to [33:33], see the Sunni Hadeeth below regarding that verse:
'A'isha reported that Allah's Apostle (may peace be upon him) went out one norning wearing a striped cloak of the black camel's hair that there came hasan b. 'ali. He wrapped hitn under it, then came Husain and he wrapped him under it along with the other one (hasan). Then came fatima and he took her under it, then came 'ali and he also took him under it and then said: Allah only desires to take away any uncleanliness from you, O people of the household, and purify you (thorough purifying) (Sahih Muslim, Book 031, Hadith 5955)
and then you can easily understnad the wisdom behind the famous Hadeeth of two weighty things as is discussed in this answer:
From the Arabic page on Wikipedia:
روي عن أبو النصر عن إبن طلحة عن الأعمش عن عطية العوفي عن أبي سعيد الخذري في حديث عن محمد أنه قال: إنّي أُوشكُ أن أُدعى فأُجيب، وإني تاركٌ فيكم الثَّقَلَين، كتابَ اللهِ عَزَّ وجَلَّ، وعِتْرَتي، كتاب الله حَبلٌ ممدود من السماء إلى الأرض، وعترتي أَهْلُ بيتي، وإن اللطيف الخبير أَخبرني أَنهما لَن يفترقا حتى يَرِدا عليّ الحوض، فَانْظُرُوني بِمَ تَخلُفُونِي فيهما.
and similar to that from the English page on Wikipedia:
Zaid bin Arqam, narrated that the messenger of Allah . said: "Indeed, I am leaving among you, that which if you hold fast to them, you shall not be misguided after me. One of then is greater than the other: (First is) The book of Allah is a rope extended from the sky to the earth, and (the second is) my family, the people of my house (ahlul bait), and they shall not split until they meet me at the hawd, so look at how you deal with them after me."
which clearly states how Qur'aan and Ahlul Bayt peace be upon them are bounded to each other, thus Ahlul-Bayt peace be upon them are infallible and free from any sin and even error (like is Qur'aan) and they never go astray, what they say is the truth and who says another thing is the lier, and how they interpret Qur'aan is the correct way. This is also hidden in the Hadeeth that says علی مع الحق و الحق مع العلی, that is: Ali is with the truth and the truth is with Ali.
Thus in short, Qur'aan as revealed in quite understandable but not everyone can understand it and after the holy prophet peace be upon him and his household the route to understanding of Qur'aan should pass through his household peace be upon them.
UPDATE.
Actually I tried to remain straight, it is impossible for the Wise to send down a book that is not fully understandable, He could simply send down those parts that ARE understandable (a book of guidance being not fully understandable by anyone except for its writer seems like denying Allah being the Wise), so if He is the Wise and the book is understandable we should see who can understand it, everyone or only some. Then we see Allah says no one can touch it but those who are clean, thus no one reaches its depth but those completely purified from dirt of the sins, then Allah says I have guaranteed that Ahlul Bayt peace be upon them are such. So reasonable we should seek for their interpretation of Qur'aan, if someone's claim is right that their interpretation is lost then again one can doubt if Allah is the Wise, as He has sent His book with describers that are unreachable! So not only the book is guarded as sent, the interpretation of them also should be available and whoever claim them being completely lost is indeed trying to turn off the light of guidance:
يُرِيدُونَ أَن يُطْفِئُوا نُورَ اللَّـهِ بِأَفْوَاهِهِمْ وَيَأْبَى اللَّـهُ إِلَّا أَن يُتِمَّ نُورَهُ وَلَوْ كَرِهَ الْكَافِرُونَ
Fain would they extinguish Allah's light with their mouths, but Allah will not allow but that His light should be perfected, even though the Unbelievers may detest (it). [9:32]
