Communities outside Eretz Yisrael begin reciting the section of "Barech Alenu" in the Amida in place of "Barechenu" on the night of December 4th. This is as opposed to communities in Eretz Yisrael, that make this switch earlier, on 7th Marheshvan.
Generally speaking, a person who mistakenly recited "Barechenu" when he was to have recited "Barech Alenu" must repeat the Amida. Since he did not recite a proper Amida prayer, he is considered as though he did not recite the Amida at all, and must therefore recite the Amida again with "Barech Alenu."
The Halachic authorities discuss the question of whether or not this applies to one who mistakenly recited "Barechenu" during Arbit on the night of December 4th. The Peri Hadash (commentary to the Shulhan Aruch by Rav Hizkiya Da Silva, 1659-1698), in Siman 117, held that in this case one does not repeat the Amida. The reason, he explains, is that the Re’avya (Rabbi Eliezer Ben Yoel, Germany, 1140-1225) held that one begins reciting "Barech Alenu" only during Shaharit on the morning of December 4th. According to this view, one does not recite "Barech Alenu" during Arbit the night of December 4th. The Peri Hadash maintained that although we do not follow this view of the Re’avya, nevertheless, if one mistakenly did not recite "Barech Alenu" on the night of December 4th, he may rely on the Re’avya’s view after the fact. As such, one does not repeat the Amida in this case.
However, the Zera Emet (Rabbi Yishmael Hakohen of Modona, Italy, 18th century) disputed this ruling of the Peri Hadash. He argued that in this situation, we have a "Sefek Sefeka" ("double doubt") that warrants repeating the Amida. Firstly, Halacha may not follow the Re’avya, and may instead follow those opinions that require reciting "Barech Alenu" even during Arbit the night of December 4th. Additionally, there are those who held that even in the Diaspora one begins reciting "Barech Alenu" on 7th Marheshvan, and not on December 4th. We thus have two possible arguments that would require repeating the Amida in this case, and the Zera Emet therefore maintained that one who mistakenly recites "Barechenu" on the night of December 4th should repeat the Amida. This is also the position of several other authorities, including the Hida (both in Kesher Gadol and Mahazik Beracha), the Bet Obed and Peri Megadim.
As for the final Halacha, several authorities rule that in such a case one should repeat the Amida and stipulate that if Halacha follows the view of the Peri Hadash, the prayer should be considered a "Tefilat Nedaba" (voluntary prayer). This is the ruling of the Shalmeh Sibur, Rabbi Haim Palachi (in Mo’ed Le’kol Hai) and Hacham Ovadia Yosef.
Similarly, if a person this situation did not repeat the Amida, he should recite a second Amida at Shaharit the next morning and make the condition described above. According to the ruling of the Zera Emet, a person in this case is considered not to have recited Arbit at all, and is therefore required to recite a second Amida at Shaharit the next morning. Therefore, in order to satisfy this view, he should recite a second Amida at Shaharit and stipulate that according to the Peri Hadash, the Amida should be considered a voluntary prayer.
Summary: Jews in the Diaspora begin reciting "Barech Alenu" in place of "Barechenu" on the night of December 4th. One who mistakenly recited "Barechenu" when he was to have recited "Barech Alenu" must repeat the Amida. However, according to some views, one does not repeat the Amida if this occurred during Arbit on the night of December 4th. Therefore, in such a case one should stipulate before reciting the Amida that it should be considered a voluntary prayer according to the opinion that he is not required to repeat the Amida.
