After installing AnyVar, WP-Cache stopped serving up any files from the cache.
I believe the output buffer in anyvar_ob_start() is the cause.
Since I only cared about variable substitution in post content, changing the code to hook a content filter instead of using an output buffer solved the problem:
else
{
//add_action('template_redirect',array(&$this,'anyvar_ob_start'));
add_filter('the_content', array(&$this,'anyvar_callback'));
}