Why don't we count two nights each night, if there was always a Safek (doubt) what the date is.
In other words: if we are not sure when the second night of Pesach is, why don't we carry that doubt throughout the entire duration of Sefira?
From Nefesh HaRav by Rabbi Herschel Schachter, shlita,:
"The Rishonim [end of Tractate Pesachim] ask the following: 'Why don't we count Sefirat HaOmer each night twice [i.e., "today is the second day," and "today is the first day," etc.] due to the doubtful day?'
"HaRav Joseph B. Soloveitchik, zt"l, heard a reason why we do not do so from the Kovno Rav [see Devar Avraham]: If a person counts twice due to doubt, i.e., stating that it is either the fourth day of the Omer or the fifth day of the Omer, he will not have fulfilled his mitzva at all because a doubtful count is not considered a count. Our Sages stated in the first perek of Bava Metzia regarding ma'aser behema that it must be the tenth of every ten animals, and not a doubtful tenth."
In conclusion, now that we have an established calendar and our celebration of two days Yom Tov is only due to the minhag of our fathers, as noted in the beginning of Tractate Beitza, we count consecutive numbers each night, starting from the second night of Pesach until we have counted seven complete weeks - to Shavuot
Taame Haminhagim 577 answers (in my own loose translation):
… because we shouldn't be so strict about it, since it's nothing but a remembrance to what was done when we had the bes hamikdash.
Another [reason] is that if we count one day ahead then we'll reach number 49 on Shavuos, which we'll therefore come to treat lightly. (Avudraham.)
He then offers a reason of his own. I'll quote it, but I don't understand it:
If we count twice in one day, then one will need to count "today is the second day" on the third day, and, in case the first day is the true [first day], he'll need to count "today is the third day" with a blessing on the third day. And likewise for every day.
We also do not say Ushpizin twice each night on Succos. This would seem to indicate that although we have Sefeika DeYoma we do not extend it to either the Omer or the Ushpizin.