songdogtech on "Too many MySQL connections and MySQL server has gone away"

We *think* this may be related to maxed out MySQL connections

It is.

We have a server of about 100+ WordPress sites running. Any ideas on how we can configure MySQL/the server to handle this better?

You need to dig into server admin and configure MySQL (via my.cnf) for high loads and apache (httpd,conf) for keep alive and number of servers started. You may also not have enough hardware - RAM and CPU - for what you're doing with over a hundred sites, depending on the amount of traffic you're getting and the kind of database-intensive plugins you're using, like Feed WordPress.