The line in question was..
my( $fUploadedFileHandle ) = $query->upload( 'file' );
.. and I was generating a line in the web server logs ..
CGI::upload: syntax error at cgindex.cgi line 1539
Some time later, after trying to pawn it off on someone else, I finally checked out the CGI.pm bugs page, and sure enough the latest version, v3.21, has a simple typo bug in it. Until a new revision is released, running the supplied patch works just dandy.