Nothing really is visible until you get the assembly taken apart and try pushing back the caliper piston. And then having someone lightly push the brakes and watch its action.
I'd say it is a problem most often diagnosed by the symptoms. And if the mechanic doesn't associate pulling and shaking with a stuck piston against warped rotors, they're just going to replace what they can SEE is bad.
You probably have to explain all the symptoms and also what has been done to the car so far. Then emphasize the heat, shaking and pulling to one side and tell them they need to thoroughly check the brake calipers.
Disc brakes are great when they are working like they are supposed to, but nobody seems to have found a sure-fire way to prevent stuck caliper pistons. It can happen due to light corrosion, improper manufacture, overextention and then twisting, and foreign object.
Relatively easy to test though when the brake assembly is taken apart and the mechanic takes the time to test the action of the caliper.