On special days, prayers that pertain to that specific day are added. There are additions that, if forgotten, prevent one’s fulfillment of his obligation, and there are additions that l’chatchilah must be recited, but b’dieved, if not included, do not prevent a person from fulfilling his obligation.
On Chol HaMo’ed Pesach and Sukkot, the Ya’aleh V’Yavo prayer is added in Birkat Retzeh. If a person forgets to say it, he must repeat the Amidah. If he did not finish the Amidah yet, he goes back to Retzeh, recites Ya’aleh V’Yavo, and from there continues on until the end of the Amidah. Similarly, we recite Ya’aleh V’Yavo on Rosh Chodesh. If it was omitted in Shacharit or Minchah, the Amidah must be repeated. However, if forgotten in Ma’ariv of Rosh Chodesh, it is not recited again, because when the new month was sanctified in Jerusalem based on the testimony of witnesses, there was no sanctification at night. Therefore, the sanctity of Rosh Chodesh does not yet apply in Ma’ariv (Shulchan Aruch 422:1).
On Motza’ei Shabbat we add the Havdalah wording in Birkat Attah Chonen of the Amidah. If forgotten, it is not repeated since the person praying will fulfill his obligation afterwards, in the Havdalah ceremony performed over wine (Shulchan Aruch 294:1).
On Chanukah and Purim, Al HaNisim is added in Birkat HaHoda’ah. If a person forgets to recite it, he does not go back, since these holidays are rabbinic. Therefore, forgetting to mention them in the Amidah does not prevent one from fulfilling his obligation (Shulchan Aruch 682:1).
On fast days, individuals add Aneinu in the berachah of Shome’a Tefillah. Ashkenazim only recite it in Minchah (Rama 565:3). Sephardim recite it throughout the whole fast: on Tish’ah B’Av – in Ma’ariv, Shacharit, and Minchah; on the other fast days – in Shacharit and Minchah (Kaf HaChaim 565:17). Some are accustomed to reciting it in Ma’ariv on all fast days (Rav Rakach, Maharitz). According to all minhagim, one who forgets to say Aneinu does not repeat the Amidah.
During the Ten Days of Repentance, which are days of judgment, for during that time Hashem’s Kingdom is revealed in the world, we conclude the third berachah with the words, “HaMelech HaKadosh,” and conclude Birkat Hashivah Shofteinu with the words, “HaMelech HaMishpat.” If one mistakenly says “HaKel HaKadosh” in the third berachah and does not correct himself as he recites it (toch k’dei dibur), he must return to the beginning of the Amidah since, as we already learned, the first three berachot are considered one unit and anyone who makes a mistake in one of them must go back to the beginning. If a person accidentally concludes Birkat Hashivah Shofteinu as usual, “Melech ohev tzedakah u’mishpat” and does not correct himself while reciting it (toch k’dei dibur), according to the custom of Ashkenazim and some Sephardim, b’dieved he fulfills his obligation, because even in the wording recited throughout the whole year, the word “Melech” (King) is used (Rama 118:1; Ben Ish Chai, Nitzavim 19; Kaf HaChaim 1). Other Sephardim maintain that he does not fulfill his obligation because he did not recite the High Holy Days wording. Therefore, if he has not yet finished his Amidah, he must return to Birkat Hashivah Shofteinu, conclude it appropriately, and continue from there until the end of the Amidah. If he already finished reciting the Amidah, he must pray again, while stipulating that if he was not obligated to repeat the prayer, the second prayer is considered voluntary (nedavah) (Shulchan Aruch 118:1; Yechaveh Da’at 1:57).
There are four other additions made during the Ten Days of Repentance: “Zochreinu,” “Mi Kamocha,” “U’chetov,” and “B’Sefer Chaim.” If any of them are forgotten, the Amidah is not repeated (Shulchan Aruch 582:5).
If a person accidentally recites Ya’aleh V’Yavo, Zochreinu, or Al HaNisim on a regular weekday, he must go back to the beginning of the berachah. If he already went on to the next berachah, he continues despite his mistake.