Furniture, Wood and Cabinetry Finishing - plastic interaction with veneer top dining table?

The top of the dining table was covered with a transperent but good quality plastic sheet. Before placing the plastic sheet over the table we had put cloth place mats. We notice that over a period of a year the plastic sheet sticks to the table top wherever the place mats are not there and the finish of the table top has got sticky and kind of spotty ( when surface viewed at an angle ). Places where the place mat were there look good. Please explain whether the plastic has interacted with the finish or is it moisture trapped beneath the plastic sheet, and how to correct the finish and make it look even. The table top has got a mahogany veneer, purchased from costco.

have you tried to remove everything from the table top
and let it dry/air out?
can you move the finish with your finger where it is "sticky"?
if you can move the finish then you most likely will
have to strip the top and refinish.
the plastic has trapped moisture.
next time try a pad for the "whole" table top
or not use anything except for the place settings.

PVC migration from plastic can damage finish and discolor wood.