How to dump/log default values that are passed to hooks/filter functions?

If you want to keep your log on the server, try using php’s error_log() which is more flexible than just writing to files on disk. Something along the lines of:

add_filter('manage_edit-member_columns', 'set_custom_edit_member_columns');

function set_custom_edit_member_columns($columns) {

    error_log(print_r($columns,true),3,__DIR__."/log.txt");

    $columns['photo'] = "Photo";

    return $columns;

}

OTOH, if you find the browser console more convenient, you should include a js script to console.log() your data. Like so:

$log_msgs=array();

add_filter('manage_edit-member_columns', 'set_custom_edit_member_columns');

function set_custom_edit_member_columns($columns) {
    global $log_msgs;

    $log_msgs[]=json_encode($columns);

    $columns['photo'] = "Photo";

    return $columns;

}

function console_log_msgs()
  {
  global $log_msgs;
  foreach($log_msgs as $msg)
    echo "<script>console.log($msg);</script>";
  }

add_action('wp_footer','console_log_msgs');

(didn’t test the above code, but you get the idea)