After the recitation of the Amida during the Friday night Arbit service, the Hazan recites a special Beracha called "Me’en Sheba."
The Shulhan Aruch (Orah Haim 268) rules that under certain circumstances, a person is able to listen to the Hazan’s recitation of "Me’en Sheba" to fulfill his obligation to recite the Amida. If a person mistakenly recited the regular weekday Amida on Friday night, instead of the special text for Shabbat, and he made no mention of Shabbat in his Amida, then he may fulfill his obligation by listening to the Hazan’s recitation of "Me’en Sheba." He should stand near the Hazan to hear every word, and this can count as his recitation of the Amida. Of course, he should preferably pray the Amida himself, but he can also fulfill his obligation by listening to the Hazan’s recitation of "Me’en Sheba."
This option is not available if Friday night is also Yom Tob. Since no mention is made of Yom Tob in the text of "Me’en Sheba," one who mistakenly recited the weekday Amida on Friday night that is Yom Tob cannot fulfill his obligation by listening to the recitation of "Me’en Sheba." This point is made by the Be’ur Halacha (268) and by Hacham Ovadia Yosef, in Hazon Ovadia – Shabbat (vol. 1, p. 390).
There is also a situation where one must listen to the Hazan’s recitation of "Me’en Sheba" in lieu of the Amida, namely, if one forgot to recite "Ya’aleh Ve’yabo" during Minha on Ereb Shabbat that was Rosh Hodesh. There is a debate among the Halachic authorities as to whether a person who forgot to include "Ya’aleh Ve’yabo" in Minha on Rosh Hodesh and remembered after sundown must recite an additional Amida at Arbit that night. According to some authorities, since that night is not Rosh Hodesh, and thus one cannot recite "Ya’aleh Ve’yabo" at night, there is no purpose served by reciting an extra Amida. Others, however, maintain that the person in this case is considered to have not prayed Minha at all, and he must therefore recite an extra Amida at Arbit to make up the missed prayer. The accepted practice in such a case is to recite the extra Amida on condition that if the prayer is not required, it should be considered a Nedaba – a voluntary prayer. If this occurred on Friday night, however, this solution cannot be used, as it is forbidden to recite voluntary Amida prayers on Shabbat. Therefore, if one forgot to recite "Ya’aleh Ve’yabo" at Minha when Friday is Rosh Hodesh, his only option is to listen to the Hazan’s recitation of "Me’en Sheba" and have that recitation count as the extra Amida which he is required to recite according to some Halachic authorities. This is the ruling of Hacham Ben Sion Abba Shaul (Israel, 1923-1998).
Summary: If a person mistakenly recited the weekday Amida on Friday night, he should preferably then recite the correct Amida, but he may also fulfill his obligation by listening to the Hazan’s recitation of "Me’en Sheba," unless Friday night is also Yom Tob. If Friday was Rosh Hodesh but Shabbat is not Rosh Hodesh, and one mistakenly omitted "Ya’aleh Ve’yabo" during Minha and realized his mistake only after sundown, he should listen to "Me’en Sheba" and have in mind to make up the missed prayer through this recitation.
