If one is unsure of the date, is it valid to count both days out of doubt, and may a blessing be recited?
Some Poskim rule that an indefinite count is invalid, and hence it is invalid to count two dates out of doubt. Other Poskim however rule that such a count is valid. Practically some Poskim conclude one is to count without a blessing. According to all if after counting one verified which of the two dates were correct one is not to recount that day with a blessing. On the future nights, after verifying the definite date, one may continue to count with a blessing.
Why in the Diaspora do people not count two days due to Sfeka Deyoma?
The Rishonim explain that the reason is because this would belittle the holiday of Shavuos, as one would have to count Sefira on the first night of Shavuos. Some explain that this is because the Sefira is only valid if one counts a single definite date, and hence counting two dates would invalidate the Sefirah. Some explain based on this that in the times of the Temple, when the month was sanctified based on witnesses of the moon, many countries in the Diaspora did not count Sefira at all, as they simply were not sure of the dates. Others explain however that certainly they counted the Sefira with a blessing, and counted both days due to doubt. Some explain the reason we do not count two days in the Diaspora is because the counting today is only Rabbinical.
 Avnei Nezer Yoreh Deah 248; Arugas Bosem 168; See Dvar Avraham 1/34; Shaarey Tziyon 5681 3-4/17; Shaarey Yosher Shaar Hasfeikos 5; Keren Ledavid 140; Betzel Hachamah 5/100; Beis Avi 4/65; See Piskeiy Teshuvos 489/17; Nitei Gavriel 35/20
 Igros Kodesh 17/265 [printed in Shulchan Menachem 3/2]; Shealas Shlomo 49; Pekudas Elazer 489; See Dvar Avraham ibid; Minchas Yitzchak 8/48; Kinyan Torah 2/3; Mishmeres Shalom 36/6
 The proof: As the Raza [Baal Hamaor] and Ran explain the reason for not counting two days in the Diaspora is not due to it being invalid to count two dates but due to the mix-up it would cause with Shavuos. [Pekudas Elazar ibid] Alternatively one must conclude that it is valid as otherwise no Jews in the Diaspora ever fulfilled the Mitzvah of Sefiras HaOmer in the times of the Sanhedrin due to Sfeka Deyoma.
 Pekudas Elazer 489; Dvar Avraham ibid; Shealas Shlomo 49; Arugas Bosem 168; See Dvar Avraham 1/34; Shaarey Tziyon 5681 3-4/17; Shaarey Yosher Shaar Hasfeikos 5; Keren Ledavid 140; Betzel Hachamah 5/100; Beis Avi 4/65; See Piskeiy Teshuvos 489/17; Nitei Gavriel 35/20
Other Poskim: The Rebbe ibid and Sheilas Shalom ibid imply one is to count with a blessing.
 The reason: To suspect for those opinions that hold it is invalid, and due to the interval between the two dates and the blessing. [Pekudas Elazar ibid] However see Admur 489/21 that the first mistaken Sefira is not an interval.
 Minchas Yitzchak 8/48
 Nitei Gavriel 35/20; As it is a Sfek Sfeka, as it is disputed in Achronim as to whether one fulfills his obligation with a questionable count.
 Raza [Baal Hamaor] and Ran on end of Pesachim
 Avnei Nezer Y.D. 248
 Dvar Avraham ibid
 Igros Kodesh 17/265 [printed in Shulchan Menachem 3/2]; Mishmeres Shalom 36/1; Sheilas Shalom 49
 Birkeiy Yosef 489/4