If somebody forgot to count one night of the Omer, and did not count the entire next day, then henceforth he counts each night without reciting Beracha. Since some Rishonim (Medieval Halachic authorities) maintained that all the days of Sefirat Ha’omer comprise a single Misva, such that one who misses even a single day can no longer fulfill the Misva, the Beracha is not recited on the subsequent nights once a day has been missed.
The question arises as to whether a person in this position may recite the Beracha if he is counting on behalf of others. Even though he normally does not recite a Beracha over his own counting, perhaps he may recite the Beracha if others will be listening to his Beracha and his Omer counting for the purpose of fulfilling their obligation.
The Peri Hadash (Rav Hizkiya Da Silva, 1659-1698) ruled that since the person in this situation is not obligated to recite the Beracha over Sefirat Ha’omer, he is not eligible to recite this Beracjha on behalf of others. The Talmud Yerushalmi, as the Peri Hadash cites, states that a "Ben Ir" – resident of an unwalled city, who is obligated to read the Megilla on the 14th of Adar – is ineligible to read the Megilla on behalf of a "Ben Kerach" – resident of a walled city, who is obligated to read the Megilla on the 15th of Adar. Since the "Ben Ir" is not obligated to read the Megilla that day, he is unable to fulfill the obligation of a "Ben Kerach" by reading for him (and vice versa). Similarly, the Peri Hadash writes, a person who is not obligated to count the Omer with a Beracha, because he had missed a day of counting, is not eligible to recite the Beracha and count on behalf of those who are obligated.
Maharam Ibn Habib (Jerusalem, 1654-1696) disagrees, asserting that Halacha does not follow this ruling of the Yerushalmi. The principle of "Kol Yisrael Arebim Zeh La’zeh" ("all Israel are responsible for one another"), Maharam Ibn Habib writes, establishes that even one who has already fulfilled his obligation can fulfill the obligation on a fellow Jew’s behalf, because we are all responsible for each other’s Misva observance. In fact, Rashi, in the beginning of Masechet Megilla, writes that villagers, who are occasionally allowed to read the Megilla before Purim (sometimes as early as the 11th of Adar), can fulfill their obligation by hearing the reading by a "Ben Ir," who is not obligated until the 14th. By the same token, Maharam Ibn Habib rules, one who had missed a day of counting the Omer may nevertheless recite the Beracha and count on behalf of somebody else.
Hacham Ovadia Yosef brings those who refute this argument, distinguishing between a person who was obligated but discharged his obligation, and one who is altogether excluded from an obligation. While it is true that one who has already fulfilled a Misva can still fulfill the obligation for another, in the case of one who had missed a day of counting, he is no longer included in the obligation, and so he cannot recite the Beracha and count for somebody else.
Hacham Ovadia writes that although the Rabbis of Salonica allowed one who had missed a day of counting to serve as the Hazzan and count on behalf of the congregation, many other Poskim, including the Kenesset Ha’gedola (Rav Haim Banbenishti, Turkey, 1603-1673), and Rav Haim Palachi (Turkey, 1788-1868), followed the Peri Hadash’s stringent ruling. Therefore, we apply the rule of "Safek Berachot Le’hakel" – that one does not recite a Beracha when it is questionable whether it is warranted – and thus one who had missed a day of counting may not count on behalf of others.
Hacham Ovadia (Yabia Omer, vol. 8, O.C. 46:2) notes the ruling of the Shebet Ha’levi (Rav Shemuel Wosner, 1913-2015) that if the Rabbi is the one who normally recites the Beracha and counts the Omer for the congregation, he may be allowed to do so even if he had missed a day. Having somebody recite and count for the congregation in the Rabbi’s place would cause the Rabbi great embarrassment, and, in Rav Wosner’s view, the concern for "Kebod Ha’beriyot" – the Rabbi’s dignity – allows for the Rabbi to recite the Beracha in this case. Since in any event the Beracha is omitted only out of doubt – because according to one view, a person who missed a day of counting cannot fulfill the Misva of Sefirat Ha’omer on subsequent nights – the Rabbi may be allowed to recite the Beracha to avoid humiliation. Hacham Ovadia, however, does not accept this ruling, and maintains that even in the case of a Rabbi, or a regular Hazzan, who would suffer embarrassment, if he had missed a day of counting, he may not recite the Beracha and count on behalf of others.
Interestingly, Hacham Ovadia in a different context does allow the consideration of "Kebod Ha’beriyot" to override the prohibition of reciting a Beracha Le’batala (Beracha recited in vain). Elsewhere in the eighth of volume of Yabia Omer, Hacham Ovadia discusses the case of a woman who, long before meeting her husband, had an illicit relationship which resulted in a pregnancy and subsequent miscarriage. She never disclosed this information to her husband, and so after she gave birth to a firstborn son, preparations were made for a Pidyon Ha’ben ("redemption" of the firstborn). Hacham Ovadia ruled that due to the concern for "Kebod Ha’beriyot," the wife did not need to reveal this to her husband, even though he would be unnecessarily performing a Pidyon Ha’ben and thus reciting a Beracha Le’batala. The likely distinction between the two cases is that in the situation of the Pidyon Ha’ben, the woman was allowed to keep the information to herself, and not required to embarrass herself in order to prevent her husband from reciting a Beracha Le’batala. In the case of Sefirat Ha’omer, by contrast, Hacham Ovadia was not prepared to allow the Rabbi himself to knowingly recite a Beracha Le’batala in order to avoid embarrassment.
Therefore, one who had missed a day of counting may not recite the Beracha and count for others, even if he is a Rabbi or regular Hazzan who would suffer embarrassment by having somebody else count for the congregation.
Summary: One who missed an entire day of counting the Omer continues counting henceforth, but without reciting the Beracha. The person in this case may not recite the Beracha and count for others, even if he is a Rabbi or regular Hazzan who would suffer embarrassment by having somebody else count for the congregation.