As an electrician everything I do is to code, with or without a permit. If a homeowner wants me to pull a permit I charge extra but will always give them the option of pulling it themselves. If you pull the permit yourself your contractor shouldn't charge you any extra unless he can explain where he is going to have to make separate trips out to allow time for inspections. For example if he has to dig a footing and then wait a day for the inspector to come before pouring the concrete. That would be an extra trip because he could most likely do it all in one day without the inspection. Otherwise, everything he does should be exactly the same. If it isn't I would want to know why.
The bottom line is that it never hurts to have an extra set of eyes look at the work. Especially if you are unfamiliar with the construction process. The construction trade has, in general, a bad reputation and its well earned. There are a lot of guys out there that either don't know what they are doing or don't care if they are doing it right or not. The sad truth is that it is hard to tell the good ones from the bad unless you are actually in the profession.
Is there some reason why you can't pull the permit yourself. It has been my experience that most inspectors (not all, some are just jerks) are willing to help a homeowner by explaining the process. You just have to take the time to meet with them and ask the questions.