There is a machlokes rishonim whether the counting of the 49 days is one collective mitzvah or is each day for 49 days a separate mitzvah. The practical difference is if one misses a day or knows one will for sure miss a day, whether there is a mitzvah to count the remaining days. The opinion of the Ba'hag is that it is one collective mitzvah and if one misses a day one can no longer recite the brachah beforehand since one has not fulfilled the mitzvah. However, other Rishonim argue and hold that each day is an independent mitzvah. According to this opinion, if one missed a day since each day is independent from the other days one may count with a brachah (Tur OC 489, MB 489:36-37).
L'halacha, we are stringent that if one did miss a night to continue counting the following night without a brachah (SA 489:8). If one may no longer recite the brachah, it is preferable to hear the brachah from someone else (MB 489:37). It is important to note, even if one is not counting with a brachah, one must count Sefiras Ha'Omer [just without the brachah].
If one is unsure whether he missed a night, one may continue counting with a brachah (SA 489:8). This is based on the halachic concept of "safek sefeika l'kula" (that we are lenient when there are 2 doubts). [In the above case the 2 doubts are: 1) did he miss and 2) is the halachah like the Rishonim that each day is a separate mitzvah].
If one counted the wrong day, it is as he did not count (MB 489:35). Therefore, he must recount the proper day. If one does not, he would not be allowed to continue counting with a brachah [because he missed an entire day].
If one counts [in the proper way] even without the brachah, he has nevertheless fulfilled his obligation, and would not be permitted to recount that night with a brachah (SA 489:4, MB 489:22). Therefore, if one has not already counted, one needs to be very careful if someone ask him which night is it is tonight, not to answer him directly, rather say "last night was __" (SA 489:4). Since one may fulfill his obligation in any language, if he answers in another language other than Hebrew, it is considered as if he counted. [For example, "today is the 12th day"] (MB 489:20).
However, if he answered in one of the following instances, it is not considered as if he counted and may therefore recount that night with a brachah; If it was before shkiya (SA 489:4), if you just said the number [for example, 12] and did not say "today is the 12th day" (MB 489:20), If it is after the 7th day, and just the number was said but not the weeks. [for example, if on the 12th day one said "today is the 12th day" as opposed to "today is the 12th day which is 1 week and 5 days"] (MB 489:23), or if one had specific intention not to fulfill his obligation (MB 489:22).
If one answered after shkiyah but before tzaitz hakochavim, if one normally counts after tzaitz hakochavim, he most probably had intention not to fulfill his obligation (Be'ur Halachah 489:4 s.v. she'im).
If someone is unsure which day of sefira it is, and asks someone "is today __" [and it was that day], he may count with a brachah, since his intention was not to count, rather to clarify the day (Koveitz Halachos 5:10).