form what i could see you seem to have gotten a quality job
if the installer made a mistake on the exhaust and intake piping i am sure they will correct it. they did use sweep els and did a nice job running the pipes. the permit is a reasonable concern. pirmits are for your protection and to make sure the job is to code. since they are willing to pull them it does not seem they want to pull anything over on you. they should have pulled them first and not tried to get by with out pirmits but that is thier problem and they are the ones that have to explain why the job in done first. if they dont pull them in a reasonable lenth of time then i recomend you pull then and have it inspected and let the contractor explain why he did not.
with that said i still think you found a good contractor and got a quality job