Halacha requires adding the paragraph of "Reseh Ve’hahalisenu" in Birkat Hamazon at every meal eaten on Shabbat. Must one repeat Birkat Hamazon on Shabbat if he forgot to add "Reseh"?
A basic principle in Halacha establishes that if one forgot to add a required insertion in Birkat Hamazon, he must repeat Birkat Hamazon only if that meal was obligatory. For example, Halacha clearly obligates one to eat a bread meal on Friday night and on Shabbat day. Thus, if one forgot to add "Reseh" in Birkat Hamazon at one of the first two Shabbat meals, then according to all opinions he must repeat Birkat Hamazon.
With regard, however, to Se’uda Shelishit – the third Shabbat meal, which we eat after Minha on Shabbat afternoon – different opinions exist among the Halachic authorities. According to some views, one is not strictly required to eat bread at Se’uda Shelishit, and can fulfill his obligation by eating other foods, such as fruit, cake and the like. Therefore, some authorities maintain that a person who forgot to add "Reseh" in Birkat Hamazon at Se’uda Shelishit does not repeat the recitation. The Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909), however, disagreed. He noted that according to Kabbalistic teaching, the status of Se’uda Shelishit is no different from that of the other two Shabbat meals, and therefore even at Se’uda Shelishit, one who forgot to add "Reseh" must repeat Birkat Hamazon.
Hacham Ovadia Yosef applies to this question the famous rule of "Safek Berachot Le’hakel" – namely, we do not recite a Beracha in situations of doubt. Given the difference of opinions among the Halachic authorities in this regard, a person in this situation should not recite Birkat Hamazon, in order to avoid the risk of reciting Berachot Le’batala (blessings in vain).
There are some situations where even the Ben Ish Hai would agree that one should not repeat Birkat Hamazon if he forgot to add "Reseh." One such case is when a person attended an early Shabbat morning prayer service, ate his meal in the morning, and then eats another meal in the early afternoon, before Minha and Se’uda Shelishit. If at that meal the individual forgot to add "Reseh" in Birkat Hamazon, then he does not repeat Birkat Hamazon. Since this meal is certainly not required according to Halacha, he does not repeat Birkat Hamazon, even according to the Ben Ish Hai.
Another exception is a case where Se’uda Shelishit extended past sundown. In such a case, Halacha requires adding "Reseh" to Birkat Hamazon because the meal did, after all, begin on Shabbat. However, if one forgot to add "Reseh," then according to all opinions he does not repeat Birkat Hamazon, since the day has, in a certain sense, already ended.
In light of this debate between the Ben Ish Hai and Hacham Ovadia Yosef, one should ensure not to forget "Reseh" in Birkat Hamazon at Se’uda Shelishit, in order to avoid this question.
Summary: One must add "Reseh" to Birkat Hamazon at every meal on Shabbat. If one forgot to add "Reseh" at either of the first two Shabbat meals, then he must repeat Birkat Hamazon according to all views. The authorities disagree as to whether one must repeat Birkat Hamazon if he forgot to add "Reseh" at Se’uda Shelishit, so one must exercise particular care to ensure that he recites "Reseh" in Birkat Hamazon at Se’uda Shelishit.