Taking the summary from Raju K earlier on... Dictation does not work for a variety of reasons:
1) Using applications that uses secure keyboard input such as 1Password: Disabling the app restores dictation function to ML
2) Wrong audio device selected / inappropriate volume settings: setting the input source to internal microphone and adjusting the volume restores dictation function.
3) DNS settings issues: I am not sure whether if this is an Apple problem or DNS propagation issues but changing the DNS settings, either to Google DNS (8.8.8.8, 8.8.4.4) or 208.67.220.220 / 208.67.222.222 seems to restore function. Switching back to your ISP's DNS settings disables dictation.
4) Connection issues with Apple's dictation servers / ? for users located outside the USA. Connecting to the internet via a VPN connection to a server in the USA/UK/Canada restores function. Turning off VPN disables dictation again.
I belong to category 4... Have yet to get a satisfactory solution without VPN. I have emailed AppleCare but haven't received any response yet. I hope to get a solution from them soon.