I talked to my wife again and here's her full story:
She was heating up some food. When she pulled it out, she smelled burnt plastic and noticed the clip was black, but she hadn't been looking in the microwave while heating, so she didn't see it happen. She removed the food and ran it for a few seconds while looking through the door. During that time (about 5 seconds) either the clip or the rack began sparking and the clip caught on fire.
To answer your questions:
-There's no way to tell now if the rack was damaged at the clip, because it is now charred, and any damage that I will find by cleaning it might have happened during this event. But... the rest of the rack looks to be in great condition. There is no wear at any of the other clips. The only imperfection I can see is a some wear at one corner of the rack (the opposite corner from where the fire occured.) The sharpest edges are the ends of the rack wires, which appear to be in factory condition, and they run from front to back of the microwave, so the ends are not near the clips, which are on the side walls.
-It is a somewhat old appliance, and there is some wear to the interior paint, possibly from the use of abbrasive cleaners. A spot that stands out as exemplifying that is where some sheet metal bends meet, and there is a scuff about the size of the end of a pencil eraser. I haven't spotted any interior rust, chips, or sharp edges.
-The part that actually caught fire is the plastic body of the clip. There are 4 clips, 2 on each side wall. The affected clip is the rear one on the left side.
-My wife didn't mention any noises or rattling. Just sparks, fire, and then smoke.
I wonder if this is a case where we can just remove the rack and clips and keep on truckin'. Is this a sign that there might be something mechanically or electrically wrong with the appliance, or is it just as likely that it has solely to do with the parts that actually caught fire?