If you are still davening but you notice that the chazzan made a mistake (yes/no mashiv haruach during the wrong season, for example), and nobody else notices, can you interrupt your davening to correct him? Is this a valid צורך התפלה? It doesn't affect your personal davening per se, but it does affect the davening of the whole tzibbur in a more general sense.
I'd like an answer that covers several different parts of davening, but particularly shemoneh esrei and אלקי נצור since those are the most common places to be during chazarat hashatz.
Also, is the halacha different for parts that don't ruin shemoneh esrei if they're skipped, like זכרנו?
I admit the whole situation doesn't say much for the shul: the people who are supposed be paying attention to חזרת הש"ץ aren't, and the person who isn't supposed to pay attention is.
(Not from personal experience, fortunately.)