Our current practice is that if you forget to count one day of the omer (morning and night), it is still incumbent upon you to count, but you can't say a bracha.
As far as I understand, the reason for this is that there is a makhlokhet about what the mitzvah is. One opinion holds that counting each day is a mitzvah (so there are 49 mitzvot in the sefirah), while the other opinion holds that there is one mitzvah to count the whole sefirah.
Then Rav Soleveitchik comes along and says that the reason for not making a bracha on the omer if you forget a day is that counting, per se, must be sequential. Otherwise, you're just saying a number. I like this answer a lot.
But before Soleveitchik, how did we justify not making a bracha without shem u'malkhut ("atah hashem elokeinu melekh ha'olam") as we do for most disputed mitzvot?