76:15 After the repetition of the Shemoneh Esrei, it is customary to recite “Tzidkascha Tzedek,” which is made up of three verses: Psalms 119:142, 71:19 and 36:7. This is a form of accepting G-d’s judgment for three righteous men - Yosef, Moshe and David - who died at this time. If it is a day on which Tachanun would not be recited (at Mincha – OC 292:2) on weekdays, then Tzidkascha is not recited. It is, however, recited when davening with a minyan in a mourner's house. The reason for this is that to omit it would constitute a public display of mourning, which is not permitted on Shabbos.
76:16 If a person made a mistake on Shabbos or yom tov and started to say the middle brachos of the weekday Shemoneh Esrei, if he realized his error mid-bracha, he must finish that bracha and then start the appropriate middle bracha of Shabbos or yom tov. The reason for this is because it would have been appropriate for the middle brachos of Shabbos and yom tov to be like those said on weekdays and to mention the holiness of the day in the bracha of R’tzei, as we do on Rosh Chodesh and chol hamoed. However, in order to honor Shabbos and yom tov, the Sages instituted a single middle bracha in honor of the day. Therefore, one who started a weekday bracha should complete it, because saying it on Shabbos or yom tov is acceptable according to straight halacha (see Talmud Brachos 21a).