Just a thought that may make your periodic site visits go much easier for both you and the Contractors. Have a preconstruction meeting for each phase of the constrcution. So, before the earthwork (or footings or slab-on-grade or strucutral steel or roofing etc.) meet with all the trades involved in the work and discuss the plans, specifications and the "whys" behind the design selections. Once the contractors understand the reasons for certain provisions of the plans and specs and what your inspectors are looking for, you will get a much better response with a lot fewer problems. Everyone is on the same page.
A good example might be wood framing connectors. While most everyone is familiar with metal connectors for wood framing, not everyone knows how to install them correctly in each situation in the field. Review what connector goes where, how it fits and how many of what size nails go where.
As far as how many inspections for each phase of construction, that depends on the size of the job, the type of project, the type of construction and the experiance of the contractors. A minimum for any job is once a week IMHO.
Just a thought!