How can I determine why emails are sent to BadMail folder?

The Badmail folder only collects mail that has no valid recipient and no valid sender .. aka spam mostly. It's a folder of last resort where the mail server has no option but to discard it. It does that in the Badmail folder and the files are ASCII files so you can use any text editor to look at them.
Your mails sent have a valid sender (return address) so they'll never end up there. What you need to do is turn on Message Tracking (and leave it on, it's very handy). Read about it here:
http://www.msexchange.org/tutorials/Exchange-2003-Message-Tracking-Logging.html

Message tracking is enabled.  Did you see the picture in the link?  The email is coming through to a valid recipient ok, and then in the Advanced Queue it is being discarded as Badmail, and there is nothing actually in the Badmail folder.

The sender is external and is replying to an email from our user...some come through, some say what is in the picture.

picture is inintelligible

You have to open the browser full screen or maximize the picture...I see what you mean if you just click the link...

It is the message tracking for the email in question and says:

SMTP:  Message submitted to Advanced Queuing
SMTP:  Started message submission to Advanced Queuing
SMTP:  Message sent to Badmail

What messages are not getting through? From you? To you?

Thanks for the link...we are on SP2, but it appears that the KB article is still valid.  If I reconfigure it will the email in the Badmail folder actually tell me anything about why it is bad, or will it simply be the email itself?

Sembee,

Here's our mailflow:

Internet >> Ironmail appliance (strips spam, does recipient filtering, etc. etc.) >> Exchange

The emails are to a good recipient, Exchange receives them fine from Ironmail for processing, and it is random that 3 out of 10 emails from say, abc@theirdomain.com to def@mydomain.com get caught in the Advanced Queue and sent to Badmail.

It was disabled and simply logging that it went to Badmail in the message tracking logs, I "re-enabled" it yesterday per PeakPeak's link, if that's what it takes to enable it.

I have yet to see anything in Badmail as of yet, the folder still shows a modified date of 2005, so maybe nothing new has come through that would be badmail yet, but hopefully I'll see the emails and NDRs soon enough.

Should the original sender be sent an NDR as well?  They seem to act like they don't even know we aren't getting the emails correctly.

An NDR will be generated and sent back. However your appliance could be blocking the NDRs going back out again.

Simon.

Thanks all, I'll take it from here.