Audio/sound worked fine through the Thinkpad's speaker, I then plugged in headphones which worked fine, but then after unplugging the headphones, audio/sound did not play through the speaker, and plugging the headphones back in confirmed there was no audio / sound through them.
Playback through both speakers and headphones was fixed.
UPDATE:
This appears to be happening on all my Thinkpads (X20, X21, X22, X23, X24, X60, X60s, X61, X61s, X61T, T420) ever since Update Pack 5 for LMDE (Linux Mint Debian Edition) [affects Update Pack 6 as well]. I'm not certain if it is an issue with LMDE or Debian Wheezy.
The issue is that if you hardware or software (using volume control) mute the sound, you cannot unmute the sound via hardware or software volume control. The sound will appear unmuted but there is no sound.
The solution is to run alsamixer (it's a XTerm GUI app, so run from a terminal session). You should see a sound control for PulseAudio. You can toggle the sound on/off by pressing m (for mute/unmute).
This is the only way I have found to be able to unmute the sound.