Q. (See question 1879 above) If it isn't correct but someone did it anyway and he did remind many, and was mezake the rabbim, does he get a mitzva or is it a mitzva habaah beaveira?
A. As mentioned above, saying aloud small parts of the amida is not correct for a number of reasons. However if indeed it created a needed and recognizable benefit, it could be argued the after the fact it was the correct thing to do. It may be comparable to an 'Eis Laasos Lashem Heiferu Torosecha, (A time to do for Hashem; they have made null Your Torah - Tehilim 119: 126) permitting greeting with the name of Hashem." (Brochos 54a, 63a, et. al.) the permitted writing of Torah texts (Gittin 60a). It may also give an echo to "Gedoilo aveira lishma" (Nazir 23b).
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a