How to find all views that have "broken or missing handler"?
Yes, there is a debug option within Views's advanced settings that will print out debug statements via the Devel when a handler is broken.

Combined with Devel's Execute PHP block/form, you can use the execute the following snippet to enable debugging, evoke execution on all Views, and review the output messages for any broken handler warnings between each execution prompt.

// Capture/set debug settings.
$views_debug = variable_get('views_devel_output', FALSE);
$views_region = variable_get('views_devel_region', 'watchdog');
variable_set('views_devel_output', TRUE);
variable_set('views_devel_region', 'message');

// Execute all views/displays
foreach( views_get_all_views() as $view) { 
  $displays = array_keys($view-&gt;display);
  foreach($displays as $display) {
     dpm("Executing $view-&gt;name ($display):");
     $view-&gt;execute($display);
     $view = $view-&gt;clone_view();
  }
}

// Reset debug settings.
variable_set('views_devel_output', $views_debug);
variable_set('views_devel_region', $views_region);