Trying to get property of non-object in calendar_systems_form_alter()

The information you provided is not enough to find the problem. try it on a clean Drupal installation

Clearing Drupal cache solved your problem.

- Add the following code right after "$timezones = &$drupal_static_fast['timezones'];" in "/includes/common.inc" file

// Calendar Systems module new hook (The actual hook is hook_format_date this one is only a workaround to 
  // prevent incompatibility with modules that already have a function called module_name_format_date)
  foreach (module_implements('format_date_calendar_systems') AS $module) {
    $function = $module .'_format_date_calendar_systems';
    $r = $function($timestamp, $type, $format, $timezone, $langcode);
    
    if ($r != FALSE) {
      return $r;
    }
  }

#2563773: Calendar Systems Module Bug Closed as duplicated of this issue

Fixed, you can the latest dev snapshot when it became available (within an hour)