After looking into this, the problem appears to be with the way jQuery Mobile uses the href="#page" links. The default skin uses the href="#" in it and as a result they conflict with the jQuery Mobile mechanism.
Change the href="#" to href="javascript:void(0)"
For example:
<a
href="javascript:void(0)" class="jp-play" tabindex="1">play</a>
Or the whole skin here as a larger example:
<div id="jquery_jplayer_1" class="jp-jplayer"></div>
<div class="jp-audio">
<div class="jp-type-single">
<div id="jp_interface_1" class="jp-interface">
<ul class="jp-controls">
<li><a href="javascript:void(0)" class="jp-play" tabindex="1">play</a></li>
<li><a href="javascript:void(0)" class="jp-pause" tabindex="1">pause</a></li>
<li><a href="javascript:void(0)" class="jp-stop" tabindex="1">stop</a></li>
<li><a href="javascript:void(0)" class="jp-mute" tabindex="1">mute</a></li>
<li><a href="javascript:void(0)" class="jp-unmute" tabindex="1">unmute</a></li>
</ul>
<div class="jp-progress">
<div class="jp-seek-bar">
<div class="jp-play-bar"></div>
</div>
</div>
<div class="jp-volume-bar">
<div class="jp-volume-bar-value"></div>
</div>
<div class="jp-current-time"></div>
<div class="jp-duration"></div>
</div>
<div id="jp_playlist_1" class="jp-playlist">
<ul>
<li>Bubble</li>
</ul>
</div>
</div>
</div>