It's getting pretty nice around these parts for December so I decided to run the 'Vette to work yesterday.  The car started like a champ, then during idle I noticed a REALLY bad smell, like sulfur or rotten eggs.  The exhaust actually left some black residue under the tailpipes (it's done that before).  The car sputtered for a literal second like it was going to stall, then picked right back up at idle.  Drove twenty minutes to work (and back that night) without incident.  Any ideas what the problem could be?

Not sure where "this part" of the country is, but if it's cold weather climate and you have had the car stored for a while then I must ask if you stored it with a full tank or not?  If yes, their could be debris in the tank that was picked up and caused a slight obstruction in the fuel filter or fuel delivery system.  If no, it could have been a small "packet" of water caused by condensation within the tank caused by weather changes during storage.  Either way, sounds like it worked itself out.  You could replace the fuel filter, fill up the tank, put some gas treatment for water and some 'Stabil' in the tank, or just let it go until the next time you start it and see if it happens again.

The rotten eggs/sulphur smell is normally caused by the catalytic convertor, or, actually, the chemical reaction taking place inside the convertor. Different brands/types of fuel will smell different. Sounds(smells?) like a normal reaction.
May well have been some trash/moisture in the fuel to cause the "stumble". Might be a good idea to run some injector cleaner thru it before parking it for the winter.

Yeah, I thought it just might have been the proverbial "bad gas", moisture, or something simple like that also    I'm posting from PA, and the weather here has been ranging from 0* overnight to 50* during the daytime    The car has a new fuel filter, new catalytic converter, and a bottle of injector cleaner with a full tank of 93 octane  PSU 982006-12-11 12:39:22

I have an '82 as well. If it hasn't run for a while, the idle will drop down then back up again several times before the computer settles down.
As for the smell, it might be because the CAT is still new.