I would use Zend_Log and use the following strategy.
If you are using Zend_Application in your app, there is a resource for logging. You can read more about the resource here
My advice would be to choose between writing to a db or log file stream. Write your log to a db if you plan on having some sort of web interface to it, if not a flat file will do just fine.
You can setup the logging to a file with this simple example
resources.log.stream.writerName = "Stream"
resources.log.stream.writerParams.stream = APPLICATION_PATH "/../data/logs/application.log"
resources.log.stream.writerParams.mode = "a"
resources.log.stream.filterName = "Priority"
resources.log.stream.filterParams.priority = 4
Also, I would suggest sending Critical errors to an email account that is checked regularly by your development team. The company I work for sends them to [email protected] and that forwards to all of the developers from production sites.
From what I understand, you can't setup a Mail writer via a factory, so the resource won't do you any good, but you can probably set it up in your ErrorController or Bootstrap.
$mail = new Zend_Mail();
$mail->setFrom('[email protected]')
->addTo('[email protected]');
$writer = new Zend_Log_Writer_Mail($mail);
// Set subject text for use; summary of number of errors is appended to the
// subject line before sending the message.
$writer->setSubjectPrependText('Errors with script foo.php');
// Only email warning level entries and higher.
$writer->addFilter(Zend_Log::WARN);
$log = new Zend_Log();
$log->addWriter($writer);
// Something bad happened!
$log->error('unable to connect to database');
// On writer shutdown, Zend_Mail::send() is triggered to send an email with
// all log entries at or above the Zend_Log filter level.
You will need to do a little work to the above example but the optimal solution would be to grab the log resource in your bootstrap file, and add the email writer to it, instead of creating a second log instance.