This is probably because you’re running php > 5.3.1 and it doesn’t like using objects before creating them, I had the same issues, I fixed those by editing the following files of the plugin :
ajax-event-calendar.php
Line 1028, 1035 and 1039 add :
$permissions = new stdClass();
inc/admin-event.php
Line 25 add :
$event = new stdClass();
Done !