Software glitches have cast doubt on the accuracy of information used to determine schools' attendance figures and funding.
Headteachers across England were last week sending in electronic returns to the annual schools census.
After hearing of problems, the Secondary Heads Association emailed schools to ask if they had difficulties. They received 79 complaints in 24 hours about errors with data, all connected to problems upgrading their information management software.
Schools using Capita's popular Sims system, which manages data for more than two thirds of schools, had been ordered to upgrade to a new version Sims.net in time for the census.
Staff at the 79 schools complained that they noticed a range of errors after upgrading, including missing pupils or staff members, and attendance figures suggesting that only a handful of students had been in a class which was actually complete.
Westlands school, in Torquay, upgraded earlier than most schools in September last year and has reported at least 30 serious errors.
Colin Kirkman, deputy head, who has a PhD on the use of information technology systems in schools, said: "The whole school has been brought to its knees. I think we've spotted these problems earlier than others, which makes me worry about the accuracy of the data that schools are sending to the Government."
SHA said it was deeply concerned about the findings and would be reporting them to the Government.
Martin Ward, deputy general secretary of SHA, said: "We assume that there are far more schools with difficulties. Some of the issues reported are systematic. Our first priority is to make sure that schools are not penalised for problems with the system."
Capita said it had helped local authorities tackle any problems and that only 0.5 per cent of the 20,000 schools using Sims.net had reported difficulties.
Further complications were created by the decision to carry out the census on January 20, when many Muslim pupils would have been absent celebrating Eid-ul-Adha.
The Department for Education and Skills said it had advised schools they could use information from a different day if they felt the religious festival would distort their results.