Gemara

66a (Beraisa) Suggestion: Perhaps "mi'Yom Havi'achem Tisperu" teaches that we reap and bring the Omer, and we may start counting any time afterwards!

Rejection: "Me'Hachel Chermesh ba'Kamah Tachel Lispor" (you start counting from when you begin reaping).

Suggestion: Perhaps we reap, bring and count at night!

Rejection: It says "mi'Yom Havi'achem."

To fulfill both verses, we reap and count at night, and we bring during the day.

71a (Mishnah): L'Chatchilah, we cut the barley at night. If it was cut during the day, it is Kosher.

72a - Contradiction (Mishnah): The entire night is Kosher for reaping the Omer, and Haktarah of Chelev and limbs;

The general rule is, anything Kosher during the daytime is Kosher the entire day. Anything Kosher at night is Kosher the entire night.

Inference: This equates day and night. Just like daytime Mitzvos may not be done at night, nighttime Mitzvos may not be done by day!

Resolution (Rava): Our Mishnah is like Rebbi. That Mishnah is like R. Elazar b'Rebbi Shimon;

(Beraisa - Rebbi): If the Omer became Tamei (during the day), if there is more grain available, we reap it and offer it. If not, we do not publicize this. (If people know that it was brought b'Tum'ah, they might think that even Korbanos Yachid may be brought b'Tum'ah.)

R. Elazar b'Rebbi Shimon says, in either case we do not publicize this, for if the Omer was reaped improperly (i.e. during the day), it is Pasul.

(Rabah bar bar Chanah): R. Elazar b'Rebbi Shimon holds like R. Akiva, the Rebbi of his father, and like R. Yishmael:

(Mishnah - R. Akiva): Any Melachah (needed for Bris Milah) that can be done before Shabbos does not override Shabbos.

(Mishnah - R. Yishmael): (The Torah says not to plow or reap on Shabbos.) Just like plowing is optional (there is no Mitzvah to plow), also reaping. This excludes reaping the Omer. It is a Mitzvah, and it overrides Shabbos.

If an Omer reaped improperly were Kosher, reaping would not override Shabbos. We would have to reap before Shabbos!

Conclusion: If the Omer was reaped improperly, it is Pasul.

Question: Also Rebbi was a Talmid of R. Shimon! (Also he should hold like R. Akiva.)

72b - Answer: Rebbi holds that reaping the Omer does not override Shabbos.

Rishonim

Rosh (Pesachim 10:41): If one forgot and did not count the entire night, Bahag says that he counts during the day. Menachos 71a says that if the barley was cut during the day, it is Kosher. It seems that the Stam Mishnah in Megilah (brought on 72a) is primary. We infer that night-time Mitzvos are Kosher only at night. R. Gamliel and his Beis Din permitted matters of Tosefes (additions to) Shemitah (Mo'ed Katan 3b). Rav Ashi explained that he holds like R. Yishmael, who says that reaping the Omer overrides Shabbos. This shows that it is Kosher only at night, like we say in Menachos 72a. Also, R. Yochanan, who has a tradition from Sinai about plowing a tree field in Erev Shemitah (Sukah 34a), holds like R. Yishmael. Also, the Stam Mishnah in Megilah is considered clearcut Halachah (for it gives a general rule), like we find in Bava Kama 102a and Avodah Zarah 7a, regarding 'anyone who deviates, he has the lower hand.' Therefore, if one forgot and did not count the entire night, he counts during the day without a Berachah.

Tosfos (66a DH Zecher): R. Tam brought (all these) proofs against Bahag. The proof from the 'general rule' is not solid.. The Halachah does not totally follow the Mishnah in Bava Kama, regarding 'anyone who retracts, he has the lower hand.' The main reason we rule like that Mishnah (regarding one who deviates) is because it is Stam, after a Machlokes (a Mishnah in which Tana'im argue about that law). We establish R. Elazar (b'Rebbi Shimon, who disqualifies if it was reaped improperly) like R. Akiva, who says that what can be done before Shabbos is not Docheh Shabbos. Even though the Halachah follows R. Akiva (regarding this), this does not show that the Halachah follows R. Elazar, for we conclude that also Rebbi holds like R. Akiva.

Rosh (ibid.): Bahag says that if one omitted counting one day, he does not count afterwards, for we require "Temimos" (full weeks). The Ri disagrees. Every night is a Mitzvah by itself.

Tosfos (ibid.): Bahag's opinion is astounding. It cannot be correct.

Ran (Pesachim 28a DH v'Chi): Mar Yehudai says that if one did not count the first night, he does not count afterwards, for we require "Temimos". However, if he did not count another night, he counts during the day. Rav Hai Gaon disagrees. If we require Temimos, also if he forgot another day the count is deficient! Therefore, if one did not count at night, he counts during the day. Bahag agrees. They rely on the Mishnah that is Machshir an Omer reaped during the day. Since b'Di'eved reaping during the day is Kosher, also counting during the day is Kosher b'Di'eved. The Ri holds that the other Stam Mishnah is primary. Since reaping during the day is Pasul, also counting during the day is Pasul. They depend on each other, like the Beraisa says. A verse teaches that we start counting from when we begin reaping. The Seifa concludes that we reap and count at night, and offer during the day.

Beis Yosef (OC 489 DH v'Chasav Od): The Tur says that one who forgot at night counts afterwards with a Berachah. It seems that this is if he counted during the day. He could agree that if he forgot also during the day, he does not bless on future nights. However, the Tur says that Rav Hai Gaon holds like the Ri. The Ri surely permits with a Berachah, for each night is a separate Mitzvah.

Bach (489:6): Rav Sadya Gaon (the Ran brought this opinion in the name of Mar Yehudai) holds that it is one Mitzvah to count all the days. It begins on Nisan 16, and ends on Sivan 5. If he began the Mitzvah on Nisan 16, even if he forgot a day, this is not a problem. He blesses on future nights, for he merely completes the Mitzvah he began. If he forgot the first night, he cannot begin to bless afterwards, for there is no Mitzvah to begin on Nisan 17 or a later day. Since he missed the beginning, he totally lost the Mitzvah. Rav Hai Gaon holds that each night is a separate Mitzvah.

Tosfos (Megilah 20b DH Kol): Even according to the opinion that reaping the Omer is Kosher even during the day, counting is only at night. "Temimos" teaches that this is Me'akev. The weeks are complete only if one counts at night. If one skipped a night and day, he does not count again with a Berachah, for this is not Temimos.

Terumas ha'Deshen (37): If one is unsure whether he counted one night, he counts future nights with a Berachah. Surely, if he remembered and counted during the day, he counts future nights with a Berachah. This is Temimos, for he did not totally skip a day. Rather, even if he did not remember until the next night, he counts with a Berachah. We hold like Bahag, that if he surely skipped a day, he does not count any more, i.e. with a Berachah. There is no loss to count without a Berachah. This is unlike Tosfos in Menachos and the Rosh, who rule unlike Bahag. However, if it is a Safek whether one skipped a day, he may rely on Tosfos and the Rosh.

Poskim

Shulchan Aruch (OC 489:7): If one forgot to count the entire night, he counts during the day without a Berachah.

Mishnah Berurah (33): Many Poskim hold that b'Di'eved, one is Yotzei through counting during the day.

Mishnah Berurah (34): One does not bless during the day, for according to some Poskim this is l'Vatalah. However, on future nights he counts with a Berachah. It is not as if he skipped a day.

Kaf ha'Chayim (80): The Pri Chodosh holds that he counts future nights without a Berachah. The Acharonim say that he blesses. Therefore, some have the custom that after Shacharis, the Shali'ach Tzibur counts aloud last night's count, and the Tzibur counts with him.

Bi'ur Halachah (DH Shachach): Likewise, if during the day one is unsure whether he counted at night, he must count.

Kaf ha'Chayim (82): If one prayed Ma'ariv of Shabbos before night, then remembered that he did not count last night, he counts without a Berachah, and future nights with a Berachah.

Kaf ha'Chayim (83): If one remembered only Bein ha'Shemashos that he did not count, he counts without a Berachah. Many say that he counts future nights without a Berachah. We are stringent about Safek Berachos. He should try to hear the Berachah from someone else.

Shulchan Aruch (8):. If one forgot to count one day, whether the first day or another day, he counts the remaining days without a Berachah.

Mishnah Berurah (35): The same applies if one realizes that yesterday he counted the wrong day. It is as if he did not count at all.

Mishnah Berurah (37): It is proper to hear the Berachah from the Shali'ach Tzibur (or someone else who blesses), answer Amen with intent to be Yotzei, and then count.

Shulchan Aruch (ibid.): If he is unsure whether he skipped a day, he counts the remaining days with a Berachah.

Gra (DH Aval): Some say that Sefiras ha'Omer nowadays is mid'Oraisa. If one is unsure whether he said Emes v'Yatziv (he says it, for it is mid'Oraisa. If one is unsure about something mid'Rabanan, he need not repeat it - Berachos 21a). Tosfos in Menachos and the Rosh holds that Sefirah is mid'Rabanan nowadays, but they hold that even if he surely skipped a day he counts future nights, for each day is a separate Mitzvah. The Shulchan Aruch is like the opinion that one blesses on a Safek mid'Oraisa. This requires investigation. See what I wrote in Siman 688 and 67:1.

Gra (688:4 DH v'Lo): In Shabbos, Rava holds that we bless on mid'Rabanan laws that Chachamim enacted for a Safek (e.g. Demai, i.e. doubtfully tithed produce). Where they did not enact, we do not bless even on a Safek mid'Oraisa. The Rif, Rif, Rambam and Rosh hold like this, and the Shulchan Aruch rules like this in many places.

Mishnah Berurah (38): He counts with a Berachah due to a Sefek-Sefeka (two doubts). Perhaps he did not skip, and perhaps the Halachah follows the Poskim that each day is a separate Mitzvah. The same applies whenever one was obligated to count again without a Berachah, but he did not, e.g. he erred about the days but not about the nights, or vice-versa. He counts future nights with a Berachah.

Kaf ha'Chayim (88): We do not say Safek Berachos Lehakel against a custom.

Kaf ha'Chayim (89): If one did not count at night, and he is unsure whether he counted during the day, on future nights he counts without a Berachah, for there is a Sefek-Sefeka against him. (Perhaps he did not count during the day, and even if he counted, perhaps counting during the day is invalid.)

Bi'ur Halachah (DH Sofer): The Ritz Gei'us says in the name of Rav Hai Gaon that one fulfills Temimos through counting all the weeks. Also, if one omitted a night, the next night he says (e.g.) 'yesterday was night one. Tonight is night two.' Since he counted every day, this is called Temimos. Eliyahu Rabah says that it is good to do so. Other Poskim did not bring this. They hold that Temimos teaches that one always counts at night, but not that all the days are Me'akev.

Kaf ha'Chayim (91): If one should count without blessing, even if he is the fixed Shali'ach Tzibur, the Tzibur should protest that he not bless to exempt others.

Kaf ha'Chayim (94): The Birkei Yosef says that if a child became Bar Mitzvah during the Omer, he counts the future days without a Berachah. However, we hold that children count due to Chinuch, so if he counted from the beginning, he continues to count with a Berachah.

Kesav Sofer (OC 99): Seemingly, if one became Bar Mitzvah or converted during the Omer, even if he did not count beforehand he may count with a Berachah. He was exempt until now. Counting every day that he is obligated is "Temimos". R. Eliezer requires a Sukah proper for all seven days. He agrees that if one converted or became Bar Mitzvah during Chol ha'Mo'ed, he makes a Sukah, for until now he was exempt. However, he learned from a verse. Without a verse, it is not considered a Sukah for the entire Chag, even though he was exempt until now. Even if R. Eliezer learns from there to the Omer, Chachamim have no source. However, if he counted until now, even though it was Reshus (optional), it joins to be called Temimos. The same applies to one who counted without intent (according to the opinion that Mitzvos require intent), or intended not for the Mitzvah. The Noda b'Yehudah (1 OC 27) says that if an Onen was forbidden to do the Mitzvah, he may not bless afterwards, for this is not Temimos. However, what a child counted was a Mitzvah of Chinuch. Perhaps we hold like Tosfos, that due to Chinuch he is like one who was obligated. This is like one who is unsure if he missed a day; he counts with a Berachah.

Aruch ha'Shulchan (15): One who became Bar Mitzvah continues to count with a Berachah only if he counted until now with a Berachah.