The panel considered the mistake so bad it was likely to disadvantage pupils sitting the exam.
It was revealed four other external NCEA mathematics and statistics exam papers were affected by mistakes last year but not considered severe.
The review recommended strengthening processes, including not approving exams for printing without a final and formal independent check.
It also wanted decision-making about errors or late changes to examination papers to be dealt with at senior levels of the organisation.
The panel recommended overall accountability for technically correct, error-free exam papers lie with the leader of the examination paper development team.
All those setting the paper would have a specific role in ensuring exam papers were without mistakes.
The panel recommended a new checking stage in the exam-setting process, especially when late changes had taken place, and that any alterations not be approved for printing without a final, formal independent check.
Where examiners asked for late changes in examination papers, it was recommended that there were defined deadlines, and for any late requests for changes to go to NZQA senior management for approval.
The NZQA welcomed the findings and recommendations and said changes would be implemented this year.
"The panel's findings have given us a clear and objective view of the causes of the error. We are moving ahead to implement these recommendations to ensure they are fully embedded in our quality assurance processes ahead of the next examination round," said deputy chief executive Kristine Kilkelly.
Kilkelly acknowledged the stress and confusion the error in the Level 3 statistics paper could have caused the students who sat the examination.
"We apologise for that and assure students, teachers and schools that we will work hard to prevent such an error from happening again."
Markers had been issued with instructions for marking the standard to take account of the error and minimise any potential disadvantage to students, Kilkelly said.
She said results for the Level 3 statistics paper were consistent with those of previous years, indicating that the error did not affect student achievement.