While I am sure the bureaucracy surrounding such discrepancies is enormous, I’m not for sure I understand how it relates to a discussion about national IDs. A passport is effectively an optional national ID, so none of these issues would be solved by a national ID.
The Social Security Administration (SSA) issues IDs at the federal level, which are applied for using state or county issued birth certificates (as well as other ways). They sometimes make clerical errors. Those errors can propagate into other federal identity databases, such as the taxpayer record system operated by the Internal Revenue Service or the passport database operated by the Department of State.
The linkages between these systems are fragile or nonexistent, and if you are not careful about manually propagating changes between them you can end up in an inconsistent state which requires court action to rectify.
Passports are often used in lieu of social security cards because people are (correctly!) leery about using their SSN directly. I know people who have no intention of traveling internationally who have gotten passports because it’s extremely convenient to have a federally issued photo id.