Undefined index: visibility in panels_renderer_editor->get_pane_links() (line 481 of .../sites/all/modules/panels/plugins/display_renderers/panels_renderer_editor.class.php).

Update: I am not an expert at php errors, but it has something to do with user permissions. If I allow a user to "Configure access settings on Panel panes", "Configure caching settings on Panels", and "Use panel locks", the error disappears.

I think I've got to the bottom of the issue. Basically, if a user doesn't have the rights mentioned in the comment above, the $links[] array does not get the keys 'visibility', 'lock', 'cache' etc. However, in line 481 the code runs through these keys anyway and that causes an issue.

So, I've changed the code a bit to check whether these keys exist in the array by adding the following instruction:

if (array_key_exists($category, $links))

and the whole code now looks like (starting line 469):

    $dropdown_links = $links['top'];
    foreach (array(
	  'style' => 'Style',
	  'visibility' => 'Visibility rules',
	  'lock' => 'Locking',
	  'cache' => 'Caching'
    ) as $category => $label) {
       if (array_key_exists($category, $links)) {
		  $dropdown_links[] = array(
			'title' => '<hr />',
			'html' => TRUE,
		  );
		  $dropdown_links[] = array(
			'title' => '<span class="dropdown-header">' . t($label) . '</span>' . theme_links(array('links' => $links[$category], 'attributes' => array(), 'heading' => array())),
			'html' => TRUE,
			'attributes' => array('class' => array('panels-sub-menu')),
		  );
       }
    }