Plugin.php: PHP Notice: Undefined offset: 0 in

Some code on your site registers a filter or an action with invalid arguments. The errors you see happen, because add_action() or add_filter() was called with a second argument that is not a string, an object or an array.

Examples:

add_action( 'wp_head', NULL );
add_filter( 'the_content', -1 );

Disable all plugins, switch to Twenty Eleven, and re-enable everything until the errors comes back. Then find all calls to add_action() or add_filter().