**Edit: it is a serious issue **
From what you said it appears that in past you used the document, which you knew had clearly invalid personal data. You presented this document to the US consulate, received the US visa, traveled to US using this document and used it until the expiration date.
Now, when applying for the visa, you had to type in your date of birth. If you typed the invalid one matching the passport (which is most likely scenario, as otherwise either your visa would have the correct DOB, or you'd be told to get a fixed passport), this may be interpreted as "committing fraud by misrepresentation to obtain visa". Not only this will likely prevent you from getting more visas, but this is a criminal offense in the US.
This is very different from the case when an issued visa had a typo (i.e. you provided correct information, but it wasn't transferred to the visa), or the case when the information was correct at the moment you applied for the visa, but changed later (such as if you legally changed your name or DOB).
So if you used this document with invalid information until it expired, and if you also typed the invalid date of birth into your visa application, it would be quite hard to convince the Consulate that you made a honest mistake, and overlooked this. Please note that your affidavit and the evidence you're going to present basically would prove that you knowingly provided false information on a visa application.
Thus I suggest you talk to a qualified lawyer about this all, and follow his/her advice.
The old answer is below, but it doesn't seem to apply to your case, because it considers circumstantial changes (such as if your date of birth was officially changed by the court order during this time), and this is not your case.
Most likely you'd need to get a new visa. Department of State doesn't address the situation with the change of birthdate, but it does address the situation with a name change (which is obviously more common):
I changed my name. Is my U.S. visa with my old name still valid?
If your name has legally changed through marriage, divorce, or a court
ordered name change, you will need to obtain a new passport. Once you
have a new passport, the Department of State recommends that you apply
for a new U.S. visa to make it easier for you to travel to and from
the United States.
In your case it is even worse, because it is unclear to others which passport has the valid date of birth. You know the new passport has it right, but the airline or immigration officials might assume the old passport had it right, and the new one has a mistake - and they have no obligation to consider your other documents.