Hi. My site's not hosted on Zen so the set up may be different, but I get the same symptoms.
Control Panel/Statistics/Error Log appears only to show the Apache web server errors not the PHP ones. I prefer to have PHP errors emailed to me anyway, so I've not tried very hard to get it working with the $message_type set to 0.
From the documentation it would appear to to depend on the error_log directive so check in phpinfo(). There is also mention of a syslog() function which looks promising.
Ant
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