Check your domain settings in your Google Apps control panel (Domain Settings/Domain Names) to make sure the domain is listed as domain.com and not www.domain.com
Does Google send the mail for you or do you have google forward outgoing mail through a local server?
Also, send yourself emails and look at the full headers. Send emails to accounts outside the Google network (ie hotmail or yahoo or another free provider) and again look at the headers.
Is there a problem with the reply-to address or the from address or both? Is there an "on behalf of" line?
If you don't have any experience reading the full headers, post it here and others can try to help you.