How can I judge a globular cluster on the Shapley & Sawyer scale?

I don't think this is possible for visual observations, either. Harlow Shapley was a pioneer in the very early days of modern, scientific astronomy, before the transistor revolution, so there was less emphasis on quantitative parameters. If this work had been done more recently, Shapley and Sawyer probably would have taken good, deep, photometric, CCD images of their gc's, then fit a 2-D function to their integrated brightness. Parameters would probably include ellipticity, some sense of the original S-S concentration classification, and other things like squariness (technically speaking, higher moments of the distribution).

You could then do some analysis on the parameter sets of a large group of globular clusters, and see if there actually was parameteric clustering, or if they were all just distributed randomly through phase space. That would give you a logical, natural, absolutely quantitative classification scheme.

I don't think it would be a feasible task to do while you're observing a cluster through a telescope. Without being trained in this sort of thing, I think you would have to photograph the cluster or reference it some other way, and use comparisons with similar globulars to refine your classification. After looking at this table of each classification, it seems like the categories are solely qualitative and so it's just left up to your judgement.