Was it a particular year that came with the LSD?

My MCS is a 2004 but I have no clue if it has one or not.

 

The LSD was never standard equipment on any first-gen MINI except the 2006 JCW GP. It was also never included as part of any of the option packages - it had to be ordered as a separate "a la carte" option.

The factory LSD was available starting with the 2005 models, and was only available on the 'S' with the manual transmission, so your 2004 wont have it.

In short, it was available on the manual-transmission 2005-2006 'S' coupes and 2005-2008 'S' convertibles.

 

That settles that

 

And for the next question:
If one were looking at a 06 MCS which could have a LSD, how could one determine if the MCS being looked at has a LSD??

 

ASAIK.... you would have to drive it to feel it or see the original window sticker.

My prefered method is to drop the clutch at 4200 rpms and look for 2 black tire marks! 2 marksmeans both wheels were spinning due to the lsd.