Moderator Post (s) for this thread: >Gluebythiggy on 12/11/2007
There is a phenomenon called "plasticizer migration." The way I explain it to people is the the chemicals added to plastic to keep it soft and flexible leach out into the finish and do the same to it. If it comes from bubble wrap or packing foam, it's often called "packing marks." It can also occur from the little plastic feet on radios, vases, telephones, etc.
Just how to treat it depends upon how deep and bad it is. I've seen it buff out with a little rubbing or go all the way down to bare wood.
First thing I would try would be to dampen a cloth with mineral spirit or naphtha and lightly rub. If it is indeed "residue" and not finish damage, then I'd try Goo-Gone. If that doesn't work, you might need a light steel wool buffing. This is likely to alter the sheen, though, however, it may be better than what you have now.