Inspection is, in many respects, just the act of "looking". Knowing what to look for is, of course, critical. The "what" you will be looking for is primarily the design, so familiarity with design and the parameters of design will help you immensely. Unfortunately, you also have to be able to decipher designs that were done many years ago and attempt to discern the "intent" of the designer, as codes and standards were less clear in many respects than today's codes and standards.
Read codes...old and new. Read inspection manuals (ACI Manual of Concrete Inspection is a good start). Read treatises on condition assessment of existing structures (ASTM E2018 (Property Condition Assessment) and ASCE 11 ( Guideline for Structural Condition Assessment of Existing Buildings).