We use log4net for logging. I've never done this, but my understanding is you can configure it to send email using the SMTP Appender.
http://logging.apache.org/log4net/release/config-examples.html (towards the bottom of the page)
In mojoportal, logging is configured in the log4net.config file in the root of the web. I copied some of the example configurations from th above and pasted them into our log4net.config file just now and committed it to svn trunk. You may be able to uncomment and configure it to send you email.
In my experience, once your site has been up for a while you will get lots of errors caused by bots and scripts making strange requests as they poke at your site looking for vulnerabilities or trying to spam your blog or contact form and this may become very annoying as email. log4net has a progressive series of logging levels, in mojoportal it defaults to INFO but you may want to set it to ERROR to reduce the noise.