I set up a domain on Google Apps with some email addresses, and wanted to send contact information from a WordPress form that was using Formidable. However, the emails weren't being sent correctly from the form. When I sent a message from my Gmail account, the message went through correctly (I set up another email on the same domain for testing purposes).
Inspecting the mail error logs (for me on the shared hosting, was at ~/mail/new/*), I got things similar to the following: