ISO 17025 audit

You asked

How to correctly audit against ISO 17025 standard?

Effective auditing against ISO 17025 criteria involves knowledge by the auditor, of mandatory and nonmandatory requirements of ISO 17025. Auditing skill and competency is also required.

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What to look for when auditing this standard?

To audit the entire standard, go sequentially through the standard requirements using an audit checklist. Advisera has an  ISO 17025 document template: Internal Audit Checklist available at https://advisera.com/17025academy/documentation/internal-audit-checklist/ 

If ISO 17025 requires a document or record, request an example of such a document and check if it meets the requirements. If not, the finding is raised as a nonconformance. For information on the mandatory requirements have a look at the Whitepaper Checklist of mandatory documents required by ISO 17025:2017 at https://info.advisera.com/17025academy/free-download/checklist-of-mandatory-documents-required-by-iso-17025 

Also, have a look at the answer to a question at https://community.advisera.com/topic/is-personnel-in-iso-17025-required-to-have-training-and-certificate-before-starting-auditing-the-lab/

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3. Is there a difference between auditing techniques when auditing 9001 and 17025"

Auditing techniques are common for all Quality management systems. Have a look at the whitepaper How to perform an internal audit using ISO 19011 available from Advisera at https://info.advisera.com/free-download/how-to-perform-an-internal-audit-using-iso-19011 

For 17025 there is a large technical component.  Have a look at my answer at https://community.advisera.com/topic/iso-17025-auditing/  and  

ISO 17025 technical internal audit: The basics https://advisera.com/17025academy/blog/2020/11/10/iso-17025-technical-internal-audit-the-basics/