I have a Cent OS dedicated virtual server with Postfix. I also have google apps on a local domain.
When using any local applications, like PHP, to send email it will try to look up the host locally and deliver the mail internally rather than utilizing the google apps domain.
For example. A php script utilizes mail to send to localdomain.com. Postfix sees that localdomain.com is hosted on the same server. However, localdomain.com is hosted at google apps. Postfix will return an error saying 'unknown user'.
It's very simple to resolve this issue. You do not need to relay off of google apps SMTP servers.
Edit the following file (I like to use nano)
Update your transport maps if it's not set. I have Plesk installed as well, so I added hash:/etc/postfix/transport before hash:/var/spool/postfix/plesk/transport separated by a comma.
transport_maps = hash:/etc/postfix/transport, hash:/var/spool/postfix/plesk/transport
If you have made the MX changes to your domain for google apps http://www.google.com/support/a/bin/answer.py?answer=174125 , make the following addition in your /etc/postfix/transport file.
It'll force postfix to look at your MX records rather than trying to deliver the mail internally. If you use brackets  around localdomain.com in the relay it will ignore MX records (e.g. localdomain.com relay:[localdomain.com], which is good if you have your mail server locally to prevent loopbacks, but we are using google apps).
Run the following command to hash your transport file.
Reload your postfix configuration
Try sending mail and see what your results are. This is my mail log location:
tail -50 /usr/local/psa/var/log/maillog
You should see something like this:
Nov 18 00:00:00 fit postfix/smtp: 91B149F99213: to=<email@example.com>, relay=ASPMX.L.GOOGLE.COM[126.96.36.199]:25, delay=1.2, delays=0.04/0/0.28/0.84, dsn=2.0.0, status=sent (250 2.0.0 OK)