The California board regulating the practice of enginering (BPELS) has issued a "Guide to Engineering & Land Surveying for City and County Officials"
http://www.pels.ca.gov/pubs/local_officials_guide.pdf If the plan checking is limited to "...simple code compliance, non-discretionary comparison of the engineering documents with clearly mandated code requirements..." then the plan checker does not need to be a licensed engineer. On the other hand if the "...comments involve the exercise of professional engineering discretion and independent engineering judgements..." then the plan checker must be a licensed engineer or working under the direct supervision of a licensed engineer.
This may require the hiring of professional engineers to perform the engineering reviews.
Non-licensed plan checkers can still reject submittals that do not have required engeering calculations.
What you consider to be a clearly mandated code requirement and what requires engineering judgement may implact what the checker can do. Does this include simple calculations? If so where do you draw the line.
One of the points that the Guideline makes is that in California local building departments may not require the applicant retain a structural engineer as opposed to a civil engineer. A number of jurisdictions are obviously in violation of the law.
It would be interesting to understand the rules in other states. It may be that in some states that there is an exemption for government employees.