Overview#The Certificate Algorithm ID field specifies the algorithm used by the Certificate Issuer to sign the certificate, and any parameters associated with the algorithm. RFC 5280)
This rather misnamed field contains the Certificate Algorithm ID for the signature algorithm used by the Certificate Authority to sign the certificate. There doesn't seem to be much use for this field, although you should check that the Certificate Algorithm ID matches the one of the Digital Signature on the certificate Even if someone can forge the Digital Signature on the cert then they can also change the inner Certificate Algorithm ID, it's possible that this was included because of some obscure attack where someone who could convince (broken) Certificate Algorithm ID A to produce the same signature value as (secure) algorithm B (Cryptographic Collision) could change the outer, unprotected Certificate Algorithm ID from B to A, but couldn't change the inner identifier without invalidating the Digital Signature. What this would achieve is unclear.
Be very careful with your use of Object Identifiers. In many cases there are a great many OIDs available for the same Certificate Algorithm ID, but the exact OID you're supposed to use varies somewhat.
Your best bet is to copy the OIDs everyone else uses and/or use the RSADSI or X9 OIDs (rather than the OSI or OIW or any other type of OID). OTOH if you want to be proprietary while still pretending to follow a standard, use OSI OID's which are often underspecified, so you can do pretty much whatever you want with things like block formatting and padding.
Another pitfall to be aware of is that Certificate Algorithm ID which have no parameters have this specified as a NULL value rather than omitting the parameters field entirely. The reason for this is that when the 1988 syntax for AlgorithmIdentifier was translated into the 1997 syntax, the OPTIONAL associated with the AlgorithmIdentifier parameters got lost. Later it was recovered via a defect report, but by then everyone thought that algorithm parameters were mandatory. Because of this the algorithm parameters should be specified as NULL, regardless of what you read elsewhere.