I am calling "swfobject.js", "jquery-1.3.2.min.js", and "jquery.playlist.js" in that order. then...
<div id="player"></div>
<script type='text/javascript'>
var so = new SWFObject('/media/player.swf','player1','320','240','9');
so.addParam('allowfullscreen','true');
so.addParam('allowscriptaccess','always');
so.addParam('wmode','transparent');
so.addParam('seamlesstabbing','true');
so.addVariable('file','playlists/playlistfile.xml');
so.addVariable('plugins','captions-1');
so.addVariable('captions.back', 'true');
so.addVariable('captions.state', 'true');
so.addVariable('captions.fontsize', '11');
so.write('player');
</script>
<noscript>
This content requires the Adobe Flash Player v9.0 or better.
<a href="http://get.adobe.com/flashplayer/">Get Flash</a>
</noscript>
Why wont screen readers read the buttons like it does on your example page? Im using JAWS 10 to test and your example page here works fine... http://www.longtailvideo.com/support/tutorials/Playlist-Tutorial

The JavaScript Playlist Tutorial is using the default wmode, which is window.
Any particular reason that you are using wmode=transparent?
The JW FLV Player doesn't have transparency, so all wmode=transparent does, is subject the client to the Flash Player's wmode=transparent bugs.