Undeliverable mail by MS Exchange server

Question

I'm the dark horse trying to use Mail on an Exchange server at work. I spent yesterday getting the connection together, and it's all working fine except for this one thing.
Everything I send bounces back to me as undeliverable with the following message:
Your message did not reach some or all of the intended recipients.
Subject: Re:test
Sent: 6/26/2007 9:34 AM
The following recipient(s) could not be reached:
  Legitimate internal email addy on 6/26/2007 9:34 AM
  The e-mail account does not exist at the organization this message was sent to. Check the e-mail address, or contact the recipient directly to find out the correct address.
  server01.DOMAIN.local
I rarely see this notification in Mail--it shows up in my Outlook Web Access inbox. The messages I'm sending (the ones that are supposedly undeliverable) do reach their addressees, but they go straight into the user's Exchange server's automatically created "SpamEmail" folder.
I feel like something of a hero having navigated the pitfalls involved in setting this up so far, so I don't want to give up. Also, my option is to use Entourage, which was drastically slowing my quad core Mac Pro every time it checked to "Now update" somesuch thing or another--which was always, no matter how I had the "schedules" scheduled. I don't want to go back. (And webmail is o.k. for remote access, but not for daily office work.)
Thanks
Core Duo iMac 24", G4 PB, Mac Pro   Mac OS X (10.4.10)   Airport Extreme network with a Cranky Ethernet drive
Core Duo iMac 24", G4 PB, Quad Core Mac Pro   Mac OS X (10.4.10)   Airport Extreme network with a Cranky Ethernet drive

Answer 1

Without seeing the full header of one of those messages, its nearly impossible to say what's wrong and even with the full header, its not an easy issue to diagnose without more info. Your best option is to report this problem to your Exchange server's administrator and ask him or her to look at the Exchange server's log files for any issues.