(15) And from the day on which you bring the sheaf of elevation offering—the day after the sabbath—you shall count off seven weeks. They must be complete: (16) you must count until the day after the seventh week—fifty days; then you shall bring an offering of new grain to the LORD. (17) You shall bring from your settlements two loaves of bread as an elevation offering; each shall be made of two-tenths of a measure of choice flour, baked after leavening, as first fruits to the LORD.

§ The Gemara analyzes the matter itself of Abaye’s statement cited in the course of the previous discussion. Abaye said: It is a mitzva to count days, and it is also a mitzva to count weeks. The Gemara notes that in fact the Sages of the study hall of Rav Ashi counted days and they also counted weeks. Ameimar counted days but not weeks. In explanation of his practice, Ameimar said: Since there is no longer an omer offering, the counting is performed only in commemoration of the Temple. Therefore, one does not need to be so scrupulous to count both days and weeks.

[Ameimar] said the count of nowadays is not [a Torah] obligation because there is no longer a korban omer, rather it is only a remembrance for the Temple. Therefore, counting only the days should suffice.

It seems that you're able to make a bracha [and count sefira] between sunset and the tzeis hakochavim, and you don't have to wait until after tzeis since it's a doubt on a rabbinic level. He also said that it is better to count sefira during the day close to dark, in order to satisfy "completeness", but that doesn't seem proper.

In a situation where one forgot to count at night, the Ba'al Halachos Gedolos held that one could count during the day, and that also seems to be the implication of the mishna at the end of our perek (71a) which teaches that the Korban HaOmer was reaped at night, but had it been reaped by day, it would still be kosher to be brought as the korban...

...The Baal Halachos Gedolos continued that if someone missed an entire day, he should no longer count, because of the requirement of "completeness," but that is an incredibly curious position and isn't correct.

(22) It is a biblical positive command to count seven full weeks from the day that the omer is brought, as it is written: "From the day after the sabbath, the day you bring the sheaf of wave-offering, you shall count seven full weeks" (15). The days must be counted along with the weeks, as it is written: "You shall count fifty days" (16). The counting must be performed from the beginning of the day. Accordingly, one is to do the counting at night, beginning with the night preceding the sixteenth of Nisan.

(23) If one forgot and failed to count at night, he may count at daytime. The counting must be performed while standing; but if one counted while sitting, he has fulfilled his duty.

(24) Every Jew is required to perform this duty, everywhere and at all times. Women and slaves, however, are exempt from it.

(2) If they (the people who are counting) made a mistake on a cloudy day and they blessed on the counting of the Omer, they should go back to count when it got dark. Those who are punctilious, they do not count until the stars come out [namely, three stars], and this is a proper thing to do.

(3) The one who prays with the community during the day, he should count with them without a blessing. And if he remembers at night, she should bless and count. GLOSS: And even if he answered “amen” to the blessing of the community, if he had the awareness that he was not fulfilled [of his obligation], he may go back and he may bless and count that night. (Beit Yosef in the name of the Rashba)