Hi Feif Un.
I can totally understand that the “blind obedience” you talk about is not always easy to “just” follow for a variety of reasons.
I can also understand wondering if what the gedolim are always saying is always correct.
But I will give you my perspective:
Da’as Torah, whether any one of us suspects something is or not right, based on our own views, is still Da’as Torah.
While it is true that anyone can make a mistake, it does not matter that we perceive something a godol says as being in error.
Why? Because I have come to a level of faith where if something seems like an error in “stage one” of it’s impact. Or even in subsequent stages, somewhere along the line that decision, no matter how we judge it, has it’s role in providence, IF, it comes from a godol.
You are correct that only Hashem does not make mistakes. It is my understanding, that all that is, is only so because Hashem wills it to be so.
In light of this, if a ruling or opinion from a godol comes down that seems to be an error, my belief is that somewhere up the line of that rulings impact, is exactly what it was suppose to be, whether I realize it or not.
Da’as Torah, to me, is still Torah, and sacred.
That is just my view.