Recently installed Mountain Lion across all systems, dictation worked perfectly all around.
Then, after adding a new, external sound card, I must have changed my internal mic settings by accident because I was seeing the dictation mic, but it wasn't picking up my voice.
Under "Sound" preferences, I could see the mic was picking up my voice, but it wouldn't in dictation. The fix was under "Dictation and Speech" preferences, where I needed to set the dropdown to internal mic.
After reading most of this thread, I thought it also might have been a conflict/bug with a 3rd party app that I have installed, but that turned out not to be the case.
4 checks:
1. System Preferences > Sound > ensure internal mic is set to built-in and input volume is at least 50%.
Check to see that input volume is being recieved by talking and looking at the meter.
2. System Preferences > Dictation and Speech > make sure dictation is turned on and dropdown set to internal microphone.
3. Go > Utilities > Audio MIDI Setup > ensure "Built-in Microphone" has a black microphone icon next to it. If no black mic icon, right-click "Built-in Microphone" and select "Use this device for sound input". Format should be 44100.0 Hz and 2ch-24bit integer.
4. System Preference > Parental Controls > Other > ensure that "disable use of dictation" is not checked under the user that you are logging in as.