The finish paint was generally enamel. That didn't cross my mind when I mentioned it. It can heat up paint and burn it. Sometimes adhesives can stain paint. Have you tried some compound on it? Work a small spot. If the mouldings have been taped up and painted around you should be able to feel a paint edge that feels higher then where the molding was at. If it glue residue it normally feels higher then the paint. Hard to tell what you have going on there looking at your pic, but it almost looks like that side might have been sprayed with some red oxide primer and repainted with the moldings taped, and I say that because primer is a heavier base and it will travel further behind tape lines , nooks and crannies, and jambs then paint will. If that is in fact the case there is not a whole lot you can do that won't make it look worse. If it has been refinished in lacquer products as was common in the late seventies most solvents will bite back into it if your not extremely careful. If it feels like glue on top of paint , I use the 3m adhesive remover on a rag kind of soak it for a min then use a soft yellow bondo spreader to kind of give it a scraping action or a plastic razor blade.
