I don't have much experience with using Google to send and receive email with apps, but you might have to include Google's special SPF record inside your mailing domain's TXT record to send mail properly.
Google's SPF record for Apps is here.
From that page...
To create an SPF record for a domain:
Log in to the administrative console for your domain.
Locate the page from which you can update the DNS records. You may need to enable advanced settings.
Create a TXT record containing this text: v=spf1 include:_spf.google.com ~all
this is NOT a separate TXT record if you already have one, just add the include:_spf.google.com part to your existing domain an ~all if necessary)
Publishing an SPF record that uses -all instead of ~all may result in delivery problems. See Google IP address ranges for details about the addresses for the Google Apps mail servers.
If your registrar also requires a host setting (such as @), see the TXT records for specific domain providers list for precise instructions.
Save your changes.
Keep in mind that changes to DNS records may take up to 48 hours to propagate throughout the Internet.