Wordpress - Undefined offset: 0 in > [...] /wp-includes/capabilities.php on line 1067

You have found a bug in Genesis.

Your Xdebug stack trace fingers the culprit as the genesis_save_custom_fields() function which calls current_user_can() with a singular capability (edit_post and edit_page) which also requires an additional argument, in this case the post ID which is missing.

current_user_can() calls has_cap() which calls map_meta_cap() which does a switch statement on the capability name. See line 1067 of capabilities.php. The 2 undefined offset notices are from $args[0] which is not an array because the post id is missing from the current_user_can call in Genesis.

The Cannot modify header information - headers already sent warning are from Xdebug printing out the PHP notices. In fact if you were not using Xdebug you wouldn't even see the PHP notices unless you checked your logs because the error is in a function attached to save_post and the page gets refreshed which prevents Warnings / Notices / Errors from being displayed on the page even with WP_DEBUG set to true.

Fix:

On line 234 of lib/functions/options.php change:

/** Check the user allowed to edit the post or page */
if ( ( 'page' == $post->post_type && ! current_user_can( 'edit_page' ) ) || ! current_user_can( 'edit_post' ) )
    return;

To:

/** Check the user allowed to edit the post or page */
if ( ! current_user_can( 'edit_post', $post->ID ) )
    return;

Also to note, there is no need to check the post_type because the edit_page and edit_post caps are interchangeable.