We have had a chance of having the checker design an assy tool. After designing it and putting together the check package, we gave him the job to check. The mistakes were basically the same we all make, tolerance issues, typos calcs and incomplete information.
The lesson learned is that any one of a professional team would be able to repeat this process.
As of now we no longer use drawings, but do have a Model Base Definition Check list and that is first checked by the designer, then a checker will go down the list.
This has taken away some of the subjective checking that we had with a check group, and made them specific adjective points.
I don't know anything but the people that do.