couple thoughts
leading in that close to glass is touchy business, that said, its odd that a body shop would bother leading that spot,quick and cheap plastic would have been my guess, along with the bubbling paint all over the top,as if the old glue may have not been removed completly and painted over?
leading a seam is done over clean metal,looks as tho no sheet metal skin was there when they leaded, strang they didnt weld in a patch and then lead it, or plastic over the patch?
may as well pull the chrome and the headliner and have a better look around, maybe spot other rust or welds from other work that was done wrong,front glass should be pulled also, the top may be able to repaired properly, if you lack the tools,take it to 2 or 3 body shops for diff opinions.
you gotta realize a change of tops is gonna be pricey to have done and the new top WILL have dings to repair..
You might strip more paint and check if its the old glue causing bubbles , clean and prime and let a shop weld in patches and finish off seams again.
id say it was a back yard job.