Grahamy,
I'm only addressing the soffit repair in the picture here and not any other issues you may have. In the time it took everybody to type up the 27 posts here, I could have had that board replaced (not including stain/paint). It is not a big deal, not nailed to fascia,just to underside of rafter tails. A section could be cut out next to a rafter, a nailer attached and new piece installed, but he should replace the whole piece really.
I can understand why your upset. As a builder I would not have called the job done.
As a customer(which I never would be because I do all myself) I'd repair it and deduct $$ off his bill. To me that"s easier than chasing after idiots. It should not get ugly over this small repair, I would refer to it as "minor, not a big deal but needs to get done" when speaking to the builder. You've got the money!
Good Luck Man