I have some answers to Bernhard's questions about UW's mailman. We are 
running a locally modified 2.1.19 which is the latest version. I asked about 
the modifications and was told they are not related to Precedence: bulk.

The email I received on 12 Apr 2011 when I first encountered this problem has 
the following in the body:
-----
Thank you for the additional information. That was useful in figuring out 
what the problem was. I went to the sendmail log for Mailman and this is what 
I found:

Apr 12 10:18:22 mailman2 sendmail[30654]: p3CHIMsU030654: from=<roundup-
admin@web.labmed.washington.edu>, auth=no, size=2004, class=-60, nrcpts=1, 
msgid=<1302628686.17.0.575133366818.issue2384@web.labmed.washington.edu>, 
proto=ESMTP, daemon=MTA, relay=mx2.cac.washington.edu [140.142.33.18]
bash-3.2$

The message is listed as class=-60 which is Precedence: Bulk and Mailman 
discards those. Unfortunately, there isn't any way for us to change that on 
this end so the sender will need to configure their mail program such that 
this gets changed. It looks like this sender sent several messages to Mailman 
lists today and they all have that Precedence: Bulk setting and so were 
discarded.
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I was told that there is a global configuration option to specify where or 
not to drop messages containing Precedence: bulk. Obviously for us, this flag 
is set. I couldn't determine where that is located.