I took another look at the source code of this blog entry, especially the button and I discovered that the source code of the link of the button includes code of a shadowbox galery: rel="shadowbox[post-1346];player=flv;width=500;height=0;". That code gets most likely added automatically to link elements around images in your blog. Maybe another plugin or the theme adds such code snippets. It is no code of podPress.
... as you said "[...](like a shadowbox)[...]"
Try to deactivate the other plugin to see whether or not it makes a difference.
One solution might be to deactivate this button/icon and activate the text link ("Show Download Text:" on the general settings page of podPress, section "Post Content") as possibility to download the file.
BTW: The shadowbox is probably trying to open the media file in a flv player (probably a flash player). But I get an Javascript Error in my error console: "Error: uncaught exception: unknown player flv".
Maybe there is an option on the settings page of the shadowbox plugin where you can exclude audio and video files from the shadowbox.
Regards,
Tim