Add backtrace to all errors

+1 and thank you for the wonderful #301 patch. Don't forget to turn backtrace in settings at admin/config/development/logging after patch applied

Actually additions made in patch at #301 may cause crash below in theme_dblog_message() when the exception's class is not a standard one:
Object of class __PHP_Incomplete_Class could not be converted to string

As $error['exception'] is no longer used after getting its trace, I suggest we unset it then.

This new patch only adds: unset($error['exception']);

<?php
  if (isset($error['exception'])) {
    $e = $error['exception'];
    unset($error['exception']); // HERE
  }
  else {
    $e = new Exception();
  }
?>

Actually, even with my patch, some exceptions still cause what I described at #311.
I guess patch at #301 needs to be rethought to avoid this.

This new patch seems to work in all cases :-)

The 'exception' attribute is now added in _drupal_exception_handler() and directly in _drupal_decode_exception().

I'm sorry,
but it doesn't work anymore with version 7.103

This is the file generated with the rejected code:

--- includes/errors.inc
+++ includes/errors.inc
@@ -257,7 +272,11 @@ function _drupal_log_error($error, $fatal = FALSE) {
         $class = 'status';
       }
 
-      drupal_set_message(t('%type: !message in %function (line %line of %file).', $error), $class);
+      $message = '%type: !message in %function (line %line of %file).';
+      if ($backtrace_options[ERROR_REPORTING_BACKTRACE_TO_SCREEN]) {
+        $message .= '<br /><pre>@backtrace</pre>';
+      }
+      drupal_set_message(t($message, $error), $class);
     }
 
     if ($fatal) {

Attaching a re-rolled patch.

Accidentaly missed some chunks of code in my last patch. Attaching a new one.

@gresko8
Your re-rolled patch lacks my changes at #314.

Here's patch at #314 re-rolled for D7.103