When are the Pope's declarations to be followed?

I understand that Vatican I outlined the process of papal infallibility (it only works when speaking ex cathedra), and I know what ex cathedra is. But in a debate with some Protestants, I was pointed to this quote from Lumen gentium, paragraph 25 (or is it Lumen Gentium, with a capital G?):

This religious submission of mind and will must be shown in a special way to the authentic magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; that is, it must be shown in such a way that his supreme magisterium is acknowledged with reverence, the judgments made by him are sincerely adhered to, according to his manifest mind and will. His mind and will in the matter may be known either from the character of the documents, from his frequent repetition of the same doctrine, or from his manner of speaking.

So what if the Pope is flat-out wrong (and not speaking ex cathedra), and what exactly does “manifest mind and will” mean?

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