My 2003 CLK 430's metal base stem on the gear shift gets hot after driving for an hour or longer. Is that normal? I also notice a subtle, sweet alchol ordor when the transmission does a little work when I accelerate rapidly (around 5,000 rpms) or decelerate using the tiptronic. The odor goes away during regular driving. What is the odor and what is causing it?

 

Gearbox / transmission tunnel gets real hot and heat will inevitable flow through metal components over time so you feel it thru the gear shift lever. No problem.

Difficult to guess from your description of "subtle, sweet alchol ordor" but I would go for antifreeze.
Are you using any coolant. You shouldn't be.

Alternatively do you have a trans oil leak. Need to remove cover below gearbox to determine. This shield is there for a variety of reasons one being to prevent any drips on your drive. A slight damp patch on the gearbox case is not worth rectifying.