The most critical factor to check for in kashrus? is "Bedikas- Toloi'yim".
Does the Rav Hamachshir or their Representative know the hands-on practical knowledge of "bedikas toloi'yim"?
They must know thoroughly at least; a) identification of the various common insects in fruits & vegetables, b) good eyesight, c) how to use a light box, d) patience, e) how to use a shmatah bedika, f) etc.
Where was the Mashgiach trained / tested etc? ?