Unauthenticated email is not accepted from this domain
firstname.lastname@example.org,email@example.com: 550 5.7.1 Unauthenticated email is not accepted from this domain. v234s7598891wib
The cause of the problem is that:
Google rejects all mail from the @domain.com domain unless they are able to verify DKIM signature.
Add your domain.com outbound mail servers’ IP addresses under “Inbound Gateway” in the domain settings for @googlehosted.com in Google Apps.
This way you could bypass the DKIM signature authentication (or google will simply accept even if its thats not accepted.)