How to save TinyMCE fields on WordPress custom post type?

In regards to the comment @ungestaltbar posted on your question, this is what they meant. You are storing the $_POST data into variables but then not using them, rendering them useless. This won’t solve your issue but I wanted to clear that up. 🙂

Alternatively, you can see exactly what is getting passed to the next page. I cleaned up the code a bit, try this and find out if the responsibilities data is even getting passed to it. This would be the first thing I would do to debug your issue.

add_action( 'save_post', 'save_career_opportunity' );

/* When the post is saved, saves our custom data */
function save_career_opportunity( $post_id ) {

     if ( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE ) 
          return;

      if( !isset( $_POST['career_nonce'] ) || !wp_verify_nonce( $_POST['career_nonce'], 'my_meta_box_career_nonce' ) )
          return;

    if ( 'page' == $_POST['post_type'] ) {
        if ( !current_user_can( 'edit_page', $post_id ) )
            return;
    } else {
        if ( !current_user_can( 'edit_post', $post_id ) )
            return;
    }

    die( var_dump( $_POST ) ); // See exactly what is being passed to this function

    extract( $_POST );

    update_post_meta( $post_id, 'responsibilities', $responsibilities );
    update_post_meta( $post_id, 'qualifications', $qualifications );
    update_post_meta( $post_id, 'career_level', $career_level );
    update_post_meta( $post_id, 'minimum_education', $minimum_education );
    update_post_meta( $post_id, 'job_status', $job_status );

}

If not then we can safely assume it has nothing to do with the function you are using to save the post, but the issue lies with (probably) wp_editor or your meta box itself. Try this and see what happens, if you are unable to see the responsibilities data after changing your code to the above, then we may need to see more of your meta box code.