I changed the position of the header(...) lines to be above file_get_contents(...) and I think fixed the use of the file name (filename=".$file) but the image is the same. I surely have to echo the contents after getting them.
<html>
<head>
<title>Bridge Scores</title>
</head>
<body>
<a href="index.php">Back to Result List</a>
<?php
$file = $_GET['file'];
header("Content-type:application/pdf");
header("Content-Disposition:attachment; filename=".$file);
$contents = file_get_contents($file);
// note contents will have new lines so we keep these and don't
// add the <br /> tags since then we'll have an extra blank line
echo("<p><pre>");
echo($contents);
echo("</pre></p>");
?>
<a href="mailto:emitchell@ieee.org">Report Problems</a>
</body>
</html>