Microphone not working in Mac Mini after system update
Try deleting the following files...

From the root folder -

/Library/Preferences/Audio/com.apple.audio.DeviceSettings.plist

/Library/Preferences/Audio/com.apple.audio.SystemSettings.plist

From your Home folder -

/Library/Preferences/com.apple.audio.AudioMIDISetup.plist

It may be worth installing the current build of Onyx and clearing out the System and User caches before restarting your Mac. Hopefully your audio devices will be set back to their defaults and your mic will work again.