I'm using this plugin on a site where we have recently added an SSL certificate for https access to certain pages (checkout etc.).
The plugin uses WP_CONTENT_URL to add the required script tags to the page footer, but when the homepage is http, and the current page is https, this causes IE and Chrome to complain about unsecured resources being used on the page.
I've fixed it with the following code change:
wp_enqueue_script('cycle', WP_CONTENT_URL.'/plugins/wp-cycle/jquery.cycle.all.min.js', array('jquery'), '', true);
wp_enqueue_script('cycle', plugins_url('jquery.cycle.all.min.js', __FILE__), array('jquery'), '', true);
This should work for WP 2.6 and newer.
Would be nice to see this (or similar) patched into future versions.