Joe,
The course of action depends on what permit is involved and how far we got with inspections. That is why it is so important for inspectors to sign for approvals and write corrections instead of giving verbal instructions. If the permit is for something simple like a roof covering, it can be signed off without much problem. Toss in an electrical service upgrade from twelve years ago and it gets complicated.
Generally, the current code is what applies and that makes sense with some but not all situations. Let's say we're dealing with a room addition that is ten years old. It passed inspection through drywall and stopped......or did it? Is this a case where the inspector failed to sign his permit, stuck it back in the active file, got transferred, and a new guy expired the permit without following up on the job. That happens. Does this warrant applying today's code. Whatever the cause, applying a new code is punitive with a structure that got to a certain point in construction.
Now how about that service upgrade. It could be that forgetful inspector or was it corrections were more than the applicant could handle. Was inspection ever requested? Whatever the case may be, the current code is what applies.
Permits are required. First of all, the building dept. is funded by those that use the services of the dept. Secondarily, the records need to reflect what is going on. The cost of permits should be based on what amount of service will be required. The room addition that lacked only a final inspection should be not much more than an hour of dept. time whereas the el. service upgrade could be a real cluster.