Case in point... Mt. Sinai in NYC still has the largest path department in the US, 110,000 surgicals per year, as compared to, say, BWH which has 55,000.
Mt. Sinai trains good pathologists, but in my own personal opinion nowhere near as well as BWH - despite the larger volume.
Why? Well, take soft-tissue pathology. I trained (fellowship) at an institution which gets a HUGE amount of cases within my subspec., including vast amounts of consultations. That was truly great, but we sent all of our non-cookie-cutter soft-tissue cases, including consultations, to BWH, as do most a lot of other institutions, both US and international.
Thus, when Andy "Suitcase" Milonakis goes to BWH and gets his soft-tissue rotation, he can see some truly amazing things in soft-tissue and bone, and understand the finer points of which diagnosis to go with, and pertinent differentials. Will that make him better? Of course!
(however, beware: consults some places only go to fellows and attendings, in which case consultant #s is a moot point).
But back to the OP: Less than, say 15,000-20,000 surgicals per year should raise a red flag. Also, a large amount of cyto to surg specimens could spell danger, as I've heard of residents being used as "pap-smear cattle". Beyond that, talk to the current residents. They're often the best at judging if they see enough different stuff to make them competent, and if the mix between viewing yourself and going over the cases with an attending is adequate.