In particular, note that a key lemma of crystalline cohomology rests on a mistake. Experts think that it is fixable by virtue that results have depended on it for a long time and no issue was found, but it is not fixed.
I think you are trying to say that this matter has since been resolved and so presumably the whole informal proof somehow resides in literature. I suppose that to the first point you may be right (I'm guessing that it's since been made available), but to the second point I think you are overconfident that similar gaps do not exist.
I admit that my original comment was inaccurate, as it seems to suggest that the gap still exists.