Which term reflects the nature of someone who is petty or is constantly finding faults?

The term that reflects the nature of someone who is petty or constantly finding faults is "captious." This word specifically characterizes a tendency to raise objections or to criticize minor issues, often in a way that is seen as unreasonable or trivial. Essentially, a captious person delights in pointing out flaws, which aligns perfectly with the description of being petty and fault-finding.

In contrast, "denouement" refers to the final resolution or outcome of a narrative, typically found in literature or theater, and does not relate to someone's character traits. "Countenance" denotes a person's facial expression or demeanor, and while it can suggest approval or disapproval, it does not encompass the idea of being critical or nitpicky. Lastly, "calumny" involves making false statements about someone with the intent to damage their reputation, which, while negative, has a different focus than the idea of being petty or fault-finding. Thus, of all the options, "captious" is the most accurate descriptor for someone who is constantly seeking faults.