I've never looked at the error logs generated by cPanel, but figure it would be a good idea. I am talking about the log you get when you log-in to cPanel, and click on "Error Log".
The first thing to do is to make sure I'm regularly checking them, and the best way I can think of is to receive them by email. However I cannot see how to do that, and googling
cpanel receive "error log" by email doesn't turn anything up.
I suspect that this error log might be an Apache error log, in which case having it sent by email might not be possible (according to this answer).
Notes: This is a shared server, but I do have ssh access.