I'm 20 years old, a citizen of Belize, and have been to the USA countless times. I've had 2 B1/B2 visas in the past, each having been valid for 5 years. My old belizean passport (and the old US visa) have long been expired, and due to there being no Embassy of Belize in my current country of residence (Lebanon), I had to apply for a Lebanese passport in order to travel. However, there is a mistake in my new Lebanese passport, my original birth date is 1997 but the Lebanese one says 1999. I've been to the USA countless times before and I have a good record, but I'm worried that this mistake will cost me my chances of getting a visa. Will this be of any issue? My father has tried to get the birth dates right, only to be told that it can't be fixed.
It can be an issue, and it can be overlooked even when noticed. No definitive answer. The consulate knows there are problems with birthday, name spellings, and other discrepancies in applicants data. Have a good and coherent explanation when it comes up. If they smell fraud however, you could be in trouble including being essentially permanently banned from visiting the USA.
Having secondary evidence like old school reports and medical records or baptismal certificate etc which show the correct date consistently is helpful. An affidavit from an official or a priest etc are also acceptable.
From USCIS Adjudicator's Field Manual Primary and Secondary Evidence
Closely related to the best evidence rule is the concept of primary and secondary evidence. Primary evidence is evidence which on its face proves a fact. For example, the divorce certificate is primary evidence of a divorce. Secondary evidence is evidence which makes it more likely that the fact sought to be proven by the primary evidence is true, but cannot do so on its own face, without any external reference. In the above example, church records showing that an individual was divorced at a certain time would be secondary evidence of the divorce.
By evidence (such as an affidavit)
By a written statement from the appropriate issuing authority
Your young age should be somewhat helpful since you were a minor and not responsible for these mistakes.