What to do when an inspector misses stuff?

Your home inspection contract specifically states that it is not full proof. If he misses stuff, you have no legal remedy. You hire an inspector at your own risk, that's why it's important for buyers to fully research the company who is inspecting the home. That person is merely responsible for spotting things wrong with the house and giving his opinion. If his opinion is wrong, then his opinion is wrong. He did his job once the issue was spotted, whether it was by him or by you.

You decided to take his opinion for it rather than further inspecting the issue or hiring a contractor to come out. I'm not trying to come down on you, I'm just speaking from the perspective of how the law would see your case (from my understanding of my particular state's laws).

The only way you'd have a legal remedy, is if this is a.) not an "as-is" sale, and b.) the seller knew of the problem and did not put it on the property disclosure.

A home inspection is not meant to serve as a full-proof warranty on a home.