sounds like your door pins are shot. The brass bushings wear out and the door drops when it opens. The sell replacement door hinge/pin repair kits in that Red Packaged Help section in your local parts store.
Yeah, I wouldn't just loosen the door and move it up... This will just make things worse in the long run. Because the door hinges will start to wear out after the bushing is totally gone. Go to any parts store and get a bushing/pin kit. I think I spent $8.00 last time I had to do this. You can even get oversized bushings, if it is already wore out the hinges, some... Do it right the first time and save hassle in the long run.