The Ba'al haMaor (end of Pesachim) writes that there is no bracha of she'hechiyanu recited on sefiras ha'omer because we no longer have a korban ha'omer; counting sefira should evoke sadness over our loss of the Mikdash, not be celebrated with she'hechiyanu. The Akeida on this week's parsha (saw it secondhand) writes that there is in fact a bracha of she'hechiyanu on sefira. He compares sefira to the count of a zavah to become tehora -- the count of seven weeks of sefira is our purification process for the sake of kabbalas haTorah. The she'hechiyanu we recite on Shavuos is not only on the Yom Tov, but also celebrates the successful completion of sefirah (I can't think offhand of another bracha of she'hechiyanu recited only after the mitzvah is completed). Something to have in mind when you say she'hechiyanu on Shavuos night.
What if someone asks you what night of the sefira it is and you answer, "Tonight we count 15" -- have you forfeited your right to count with a bracha after that or not? R' Moshe Stern (Shu"T Be'er Moshe (3:81)) answers that you can still count with a bracha. He basis himself on a Chasam Sofer (O.C. 15) that takes issue with the Magen Avraham's chiddush that you are yotzei kiddush when you mention Shabbos in davening ma'ariv Fri night. True, says the Chasam Sofer, m'doraysa you don't need a bracha on wine for kiddush, you don't need to be b'makom seudah, but once Chazal were metakein to do the mitzvah in this fashion, a person obviouslly has no intent to be yotzei except in accordance with Chazal's dictates (we once discussed a similar idea in the Pri Megadim's pesicha ha'kolleles 3:8). Here too with respect to sefira, we use a particular formulation for the mitzvah: we mention weeks, followed by days, followed by the word la'omer or ba'omer. "Tonight we count 15" is not the formula prescribed for the mitzvah and therefore does not count. (The Be'er Moshe goes so far as to suggest that even if you just leave out the word "ba'omer" or "la'omer" you could still count with a bracha because the formula is wrong, but he is not willing to go up against the Magen Avraham who argues. In the example of night 15 (or any # past 8) you would be missing both the count of weeks as well as the la'/ba'omer, which is a more serious defect.)