I went to the "Into to the Structural Provisions of the 2006 IBC" and asked the question where "periodic" was defined. The question was waved off with a "it's in the 'Definitions' at the beginning of Chapter 17." Of course there is a definition given, but it is not particularly meaningful.
In the body of Chapter 17 there are some specifics regarding certain types of construction (high strength bolts, for example, and for welds one is referenced to AWS D1.1).
In my opinion, the entire inspection chapter is the result of bringing the UBC folks into the IBC fold. They (the UBC'ers) probably have a stronger opinion of what needs to be inspected, how often, and why. I don't posess such a strong feeling about the need or effectiveness of these "inspections".
In the end it seems to me that it is up to the EOR to specify and the Building Official to approve of the inspection program. If a liberal engineer meets up with a liberal building official the result may be not-very-frequent inspections. When everybody takes a conservative approach the cost of the special inspections may exceed the structural engineer's fee (I witnessed this happen on the design of a new High School). Sometimes it seems backwards to me that we will beat the geotech down to $15,000 for his professional recommendations, but then turn around and pay the testing arm of his firm $75,000 for field QA.