I have a mouthpiece that is over 30 years old. Although it has not been played constantly during that time, I now have a job where I use it several times each day. Recently I noticed that the black laquor has come off in places and the underlying brown base color shows. Should I be concerned? I'm guessing that this has been caused by a chemical reaction from the acids in my skin.

I don't know. Are you worried more about possibly ingesting strange substances, about your mouthpiece eventually ceasing to work properly, or about your clarinet's appearance? Since your playing seems to be earning you money, you might consider just buying a new (or alternate) mouthpiece. Compared to other clarinet parts, they're relatively inexpensive.

I used my VanDoren 360 for about 25 years and currently my VanD 5RV for about 17 years. Both had the same discolouration as you describe. Eventually the 360 got pronounced teeth marks and I needed a spare anyway, so I bought the 5RV and still use it. Never worried about the color.