In an attempt to put a stake through this one: it appears that the headers:
Accept-Ranges: bytes
ETag: "ac0f-2743f-3a2ebf5b"
cause trouble. I gather these are supposed to be server generated (in particular the "Entity-Tag" is a server(?) specific code for a file type; Accept-ranges means the server'll allow "header and some bytes more" requests), and either I'm doing them wrong or they confuse both IE and NE. If anybody has a hint ... here's the final code, FWIW:

my $debug = 0;
my $path = "/web/images";
my $file = $ENV{PATH_INFO};
$file =~ s#^[^/]*##;
$file =~ s#[^/\d-\.\w]##g;
my $pdf_file = $path . $file;
if ( -s $pdf_file ) {
  print "Content-Type: application/pdf\n";
  #print "Accept-Ranges: bytes\n";
  #print "Accept-Ranges: none\n";
  #print "ETag: \"ac0f-2743f-3a2ebf5b\"\n";
  #print "Last-Modified: Wed, 06 Dec 2000 22:36:11 GMT\n\n";
  my ($size, $mtime)  = (stat  $pdf_file)[7,9];
  print "Last-Modified: ", scalar gmtime($mtime), "GMT\n";
  print "Content-length: $size\n";
#  print "Content-disposition: attachement; filename=$pdf_file_name\n"
+;
  print "\n";

  open(PDF, "$pdf_file" ) or die "Can't open pdf $pdf_file: $!";
  print <PDF>;
  close PDF;
  print STDERR "documents: $pdf_file, $size\n" if $debug > 5;
} else {
  print "Content-Type: text/html\n";
  print "\n";
  print "<h1>Error</h1>\n
Image file : $file is missing!!!
<p>
<hr>
";

}
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