I consider felt under roof shingles to be required and I would not pay the next payment until it was done. I would tell my builder exactly that. If he refuses then maybe you can talk to your bank. I'm sure that they would be interested and refuse to pay, since if you are using a mortgage the bank is really the one buying the house. If none of this works then talk to a lawyer.
Plastic strip: I'm not sure.
Flapping and breaking: The tar won't melt and attach until the weather is warmer and the sun is hotter. Winter installations and high wind locations should have dabs of roof cement (black gook) under each tab. I'm fairly certain that these instructions appear printed on every bundle of shingles. The builder is obligated to repair the roof because it is still his until you pay, and b/c of any warantee (usually 1 year). Assuming he fixes it, I would be worried about the tabs that bent but didn't actually break and get replaced. It is likely that many are damaged from all the bending and will age and fail prematurely. One of the most important things you can do is to buy a polaroid instant camera and a lot of film and shoot shoot shoot to document everything. You might want to have a card with the date and address on it in the scene so it will show up on your photos. You might consider hiring a home inspector to look at your roof. He may say that the whole thing needs replacing.
Any builder that appears to be as slipshod as this guy needs his work checked all through the job. I hate to think of what else he has screwed up. Take lots of photos every week or every few days to document inside and out. One area of common mistakes on the sidewall flashing is shown here: http://www.jlconline.com/jlc/archive/exteriors/wrapping_house/index.html read all 5 pages.