Most of them - 100 out of 121 since 1999 - are against contracted inspection teams, which carry out most visits to schools and early-years settings. Only five were against Her Majesty's Inspectors.
Last year, Estyn carried out 435 inspections of schools, training providers, FE colleges, early-years settings, LEAs and teacher-training colleges.
Headteachers, acting alone or with their governing body, made most of the complaints (50), according to figures released following a TES Cymru request under the Freedom of Information Act. Governors accounted for another 16 complaints, with local education authorities making 21, parents and parent-teacher associations 19 and staff three.
Most complaints (53) were about the conduct of inspections carried out by contracted inspection teams, followed by concerns about the content of their reports (27) and inspection judgements (9). Five concerned both conduct and report content.
Estyn does not currently record centrally the outcome of complaints or action taken in response to them (for example, amending inspection reports), but plans to do so in future.
The National Union of Teachers Cymru has called for an end to the use of external contractors. It wants LEAs to inspect schools, with Estyn keeping a check on how well they carry out this role.
Heledd Hayes, NUT Cymru's education officer, said: "The impression we get from members is that while Estyn personnel themselves are highly professional, there is dissatisfaction with the privatised teams.
"The fact that not many complaints are received by Estyn does not mean that teachers are happy with inspection procedures. On the contrary, many find the experience frustrating and annoying but prefer to get on with the job."
Estyn consulted last month on revising its feedback and complaints procedure, and on introducing external adjudication. However, the adjudicator would not be able to overturn inspectors' judgements.
A spokesperson said: "Only a small proportion of inspections give rise to complaints but these are investigated thoroughly and, where a complaint is justified, Estyn apologises in an appropriate way and takes action to put matters right."