A slightly judgmental or emotionally-tinged adjective meaning “quick to find fault” is the word ‘captious’, which one does not encounter these days in either speech or writing but is useful withal when intending to go beyond the simple word ‘punctilious’. Its origin (according to the OED Online) and definitions are as follows:

Etymology: < French captieux or Latin captiōsus fallacious, sophistical, < captiōn-em (see caption n.).

  1. Apt to catch or take one in; fitted to ensnare or perplex in argument; designed to entrap or entangle by subtlety; fallacious, sophistical.
  2. Apt to catch at faults or take exception to actions; disposed to find fault, cavil, or raise objections; fault-finding, cavilling, carping.

In the Age of Irrationality, perhaps it is not altogether blameworthy to be captious, when the polar alternative is never to criticize despite having good reasons to do so.