Upon taking down drywall we found a lot of water damage and many framing issues that are against current code standards - headers and floor joists had to be replaced, the back of the house had to be jacked up 2 inches across a 40 yard span.

If a wood structure, then there is a wooden header behind the block and above the door that carries the weight of the building.

Your contractor will need to remove the old header, increase the size of the opening and install a new header.Good Investing...

Your header says from "PE" is this meant to be PEI?

Lots of old houses were built before codes were enforced so we see lots of things like missing headers or strange methods for hanging joists or cut out structural elements for heating ducts and things. 

I have removed a wall and installed an LVL header, and used reclaimed beams from my W2 job as support.

Oh, one thing though, where did you go to change the header at the bottom of your posts?

Be sure "My list has headers" is not clicked:Click OK.

Did the inspector actually open the walls at the headers to verify they are broken, or did he or she just make an assumption that it's structural damage?

Not ideal but he will be able to hide the header which will help to open it up.