I found a way to fix my problem. I ran sudo chown -R $(whoami) /usr/local after running brew doctor and things were corrected. I then ran brew update and things are up to date. Things are good to go.
I'm attempting to update software on my iMac with Capitan installed, using Homebrew. Every time I try I receive the error message that /usr/local must be writable. I am the admin user and have tried using sudo with no luck. Until recently I've not had this issue and was wondering if it's related...