a good mechanic will know how to CYA well enough to avoid these situations. he should have told you that the manifold and bolts were rusty, and problems could arise.
did he even do anything to prep? on a rusty cast-iron manifold, i always soak the shit out of everything with penetrating oil well before trying to remove any bolts.
frankly, if the head really does need to come off, i'd take the jackass to small claims court and make him pay for it.
The procedure basically entails taking the head off ($), clamping it securely to a drill press ($), grinding the face of the broken bolt to get an even surface if necessary ($), using a short drill bit to minimize wobble ($), drilling the broken bolt, and tapping / removing ($). And hopefully the threads are still intact.
I can't speak for newer vehicles (because I don't know what sensors it could screw up), but on anything older, loose or missing exhaust manifold bolts isn't a big deal.