This study is composed of four notes associated with using the Compatibility index of the AHP. Compatibility concerns how much two sets of priorities of an order are mutually close. (a) A case is introduced to show that inconsistency in pairwise comparisons can detrimentally effect on measuring the compatibility between the two matrices. In order to avoid such errancy, we remind readers of the meaning of Saaty’s compatibility metric and of correct usage. (b) Originating from Saaty’s consistency index for an entire hierarchy, compatibility for an entire hierarchy is derived to generalize the measurement of compatibility and its application is described. (c) The sensitivity of the Compatibility index is analyzed to figure out stable and unstable bases. A pitfall misleading to a wrong decision and its preventive action are discussed in measuring the compatibility. (d) The way of finding element to revise compatibility is suggested when consolidation is necessary after assuring inter-rater disagreement among assessors.