Starting MySQL produces "The server quit without updating PID file"
We (myself and Mr. Burning) did some diagnosis in chat, and I will detail what we did find:

The root of his problem was that MySQLd was already running in some capacity. This could have been a previous version of MySQL installed from Homebrew, still running after upgrading the binaries/libraries.

Our resolution was to simply kill all of the running processes. Then, OS X's launchd did it's work and restarted MySQLd, which was definitively running as installed by Homebrew.

That seemed to resolve the issue.