Associate assessors - senior officials from other councils who are part of the inspection teams - said there was a "tendency to see an education department as a semi-autonomous entity with its own integrated management system".
Directors also believe inspectors have yet to fully appreciate the impact of spending limits. "Education authorities work within a political context and are very dependent on politicians to take decisions and give leadership to the authority," they say.
The inspectorate, which is now halfway through the inspection of the 32 education authorities, plans to publish its own evaluation of the process next year.
In his interview with The TES Scotland this week, Graham Donaldson, senior chief inspector of education, pledged to take account of lessons from the first round of inspections.
A study of the first seven inspections compiled for the Scottish Executive by Roy Jobson, Edinburgh's director, reveals qualified support for the process and a high regard for the inspection teams who were regarded as "thoroughly professional, very experienced and of very high quality".
Directors were generally less enthusiastic about the contribution of the financial experts supplied by Audit Scotland, which helped to analyse budget management.
They were also unhappy with the public exposure of individuals in the directorate following publication of the reports and the habit of releasing two reports on the same day. That inevitably drew unfair comparisons by the media.
Half the authorities found the inspection "positive and sensitively handled" while the rest found it "overly negative and intrusive".
A key complaint remains the inspection overload on local authorities who are involved in a string of best value and quality management reviews. Directors point out that self-evaluation reports "often reflect the HMI report findings and outcomes but an issue for smaller authorities is whether they can provide and sustain the level of support needed for quality assurance in schools".
They called for greater consistency among inspection teams, better judgment and reporting of perceptions, and a shift away from the narrow focus on the improvement agenda. They were concerned that too much emphasis was placed on the views of some groups questioned by pollsters from System 3.
Associate assessors commented that "the influence of headteachers in some inspections was over-impacting on the inspection process and agenda". One authority said the final report was a "shock for the administration."
The associates, however, found final reports to be "fair and balanced" and some even considered that inspectors had erred in favour of the authority in difficult areas.