Perform boolean shape operations

I need the three logo variations combined into a single clean shape for laser cutting. Open the file, select the Artboard_Master layer, run boolean operations to unite the outer forms, subtract the inner cutouts so there are no overlapping paths, remove any zero-width or duplicate shapes, and save a new file named Logo_For_Laser.ai. Confirm the final path is a single compound path with no open subpaths.

Before I send the combined mark to manufacturing, make it easy to approve: create a version with the unite and minus-back results side-by-side, highlight any tiny islands or slivers under 0.5 mm, and note where boolean ops changed stroke widths. Add a short checklist saying whether the result is ready for die-cut or needs manual cleanup.

I ran a unite on the three logo shapes and now there are invisible holes; procurement needs a file for the vendor by Friday. I don’t know if the holes are caused by overlapping compound paths or by stray anchor points. What’s the most likely cause, what immediate boolean or pathfinder step will fix it, and how do I test the fix so the vendor doesn’t reject the dieline?

Every time I prepare marks for tooling the boolean operations leave hairline slivers and holes that force manual cleanup. Which habit around building base shapes or ordering operations should I change to reduce this cleanup, and what naming or layer convention will make it faster to spot artifacts before I hand files to the vendor?