There are 3 Additions into our Birkat Hamazon:
1. On Shabbat - we add the paragraph of “Retzei”
General Rule: The rule as to what to do if one accidently forgot these additions – is quite simple. First, you need to decide if there was a chiuv (obligation) to eat a bread meal. If there was a chiuv to eat a bread meal, then you would need to repeat the bentching. If, however, there was no chiuv to eat the bread meal then you wouldn’t need to repeat the bentching.
1. Shabbat and Yom Tov
On Shabbos and Yom Tov, there is a chiuv to eat 2 bread meals: One at night and one during the day. Therefore if one forgot the addition for either of these two meals – he would need to repeat the entire bentching. Moreover, if one is unsure whether he said the addition or not – he would need to repeat the entire thing again.
2. Rosh Chodesh and Chol Hamoed
Since there is no chiuv to eat a bread meal on these days – one would NOT repeat if he forgot the additions.
3. Chanukah and Purim
Likewise, since there is no chiuv to eat a bread meal on these days – one would NOT repeat if he forgot the additions
4. What If’s
So we see that it works in both direction, however a problem arise when we combine the two into one case:
Bedieved, if one ate a kazayit of bread both before and after sunset – some advise to only say Retzei while others say he should insert both Retzei and Yaaleh V’yavo. One should consult a local orthodox rabbi for a definitive ruling.
There is one crucial difference for men and women. Women do NOT have an obligation to eat two bread meals on Yom Tov and if they forgot – they would not repeat the birkas hamazon.
6. Midway Corrections
Now this can get complicated, so let’s organize it by 4 places of realization:
2. If one finished the 3rd bracha but did not yet begin the 4th bracha, with the word, “Baruch”
3. If he began the 4th bracha but only said the first 6 words, until the word “HaOlam”
4. Beyond that – I’m sorry, but you’ll need to repeat the entire thing