I found a way to make the messages appear - but it is far from a
useful fix to this problem. Since the "hidden" messages do appear in
the Unread Mail Search Folder, I can switch to this folder and select
the messages. I then mark them as READ, and then select them again
and mark as UNREAD. When I switch back to the Inbox, the messages all
appear (as unread, of course), and I can deal with them normally.
Given this, I think it is clear that this cannot be a filtering issue
(I have no filters set up anyway).

As an aside, my Inbox contains about 6000 messages. Could OL2007 have
a database problem for Inboxes that are so large (the PST file is
approximately 900MB)? OL2003 does not have this problem, since the
messages show up fine there.

Gomer