What should I check first?
Check the opening and all seams for continuous conductive overlap.
Can a conductive zipper leak?
Yes. Any closure can leak if the conductive path is discontinuous or the geometry creates an RF aperture.
How should I test a Faraday bag?
Test the finished bag at the actual frequency bands you need to block.
Project note: Use supplier data as a starting point. Validate the finished assembly at the relevant frequencies and environmental conditions.