I have seen a few drag cars recently in my area where there has been welding done on them (installation of patch panels, stretched wheel wells, and a filled gas doors, etc....)and after some time the weld marks show right through the paint! The odd part is the paint still feels smooth, but you can see the shape of the weld none the less.

Upon further discussion with the owners, all of the vehicles were done with mig welders and metal finished as far as possible; subsequently primed/body filler was applied and then blocked to "perfection". That seems to be the right way to do things..... So what happened? Did the bondo or primer shrink? Why would'nt you be able to feel that through the paint?

I have never seen a weld show up if it was welded completely and there was no corrosion. Chances are the patches weren't welded completely and were just spotted or stitched here and there, or the panels were lapped and corrosion is forming between the two layers and expanding. Buttwelded solid and ground near flush they will not show up. Or maybe they used laquer products that later shrunk, welds don't shrink but the fillers used to blend them in will shrink around them. Some people abuse primer surfacers trying to make them do what filler is designed for, even a good urethane surfacer will shrink if applied to heavy and sanded/painted to soon.

I agree with Bob, patch panel was just spotted in place and not fully welded.
Body filler has no to very little shrinkage.

Are you sure its from welding and NOT just sand scratches? Sand scratches would appear if you sand too soon, applied too much primer, painted too soon, wrong gun used, number of reasons.
Just because it blocked out looking fine doesnt mean it will remain looking fine

Guys, I have seen this. On my own repairs in the shop. I still to this day do now know what caused it. Though as I remember you could feel it, like a bubble. The only thing I ever came up with was that the weld retained heat, from welding, and grinding. I then put plastic filler over it and my thinking was the filler didn't get good adhesion because it hardened too quick or something like that. I started waiting a while after welding and then forgot all about it and never saw it again. I am thinking there may be something to do with the brand or quality filler. All I know is it happened a number of times to me and I haven't seen it in many, many years thank goodness.

Just a theory... The hardness of the sheetmetal will be slightly different in and around the weld than the surrounding sheet metal, whether you make full welds or spot welds. Correct me if I'm wrong, but I think MIG welding usually makes the surrounding material a bit harder.

Race cars can flex quite a bit, and if the sheet metal is harder in some places and softer in some, it might leave permanent deformation around the weld seams.

Again, just a theory...

Yes Race cars do flex alot more than your average car but I still think there was a problem with workmanship or materials that caused the welds to show. I've done work on a few tubbed and stretched nine second cars and never seen any problems. A good friend of mine has an Opel GT that he tubbed and caged, this car required a lot of sectioning. He cut it in numerous places. It runs 9.40s and is black with no hint of problems and has been done for 7 years now.