(1) I believe slavery was never allowed by God from Adam (a) till now: Most Muslims believe slavery was once allowed, some believe it's stilled allowed.
(2) Killing apostates is not allowed and was never allowed by God. Most Muslims unfortunately (going by the scholars view) believe such a rule exists.
(3) Some people (don't know how much) think because God put us nature of the religion of God, we should not seek philosophical or mystical proofs towards main beliefs. I don't hold this view, I hold we are originated upon to verify and search the truth although intuitively we do know God exists and sense a spiritual world.
(4) The nature of faith means no proofs and signs while I believe the Quran talks of faith praised only in terms of acknowledgement of proofs and signs - including signs in ourselves and horizons which are spiritual. However, all type of signs and insights are what form the foundations of faith. I hear this from atheists a lot, they define faith in a way that I don't relate to.
(5) People think the Quran stays the same so they think they understood Quran with some recitations and even think they don't need the Sunnah, ****Staff Edit**** while what I know of it, it morphs in time, for better or worse, depending on what you put into it.
(6) Most Muslims pass over or interpret in a obtuse way - what Quran says about God knowing all the future, there is verses that verify my view that not all future is known for example: "so that God will come to know the strivers from you and will come to know the patient....". I believe if future is all known then neither free-will is possible for God nor creation.
(7) Most people assume I follow scholars, because it's what most Muslims do. I semi-use them, but where there verdicts contradict Quran and goes against hadiths as well, I don't follow them.