Which term would best describe a person who shows excessive enthusiasm for minor details?

The term "obsessive" accurately describes a person who exhibits excessive enthusiasm for minor details. This word conveys a sense of preoccupation, indicating that the individual is overly fixated or consumed by specific, often trivial, aspects of a situation or task. Such behavior can manifest as an intense effort to perfect every small detail, which forms the basis of the term.

In contrast, the other terms do not relate to this characteristic effectively. "Obsolete" refers to something that is no longer in use or outdated, and does not apply to a person's behavior or attitude. "Pious" denotes a devout or religious nature, focusing more on moral virtues rather than an inclination towards minutiae. "Mediocre" describes something of only average quality and lacks the implication of excessive attention to details, which is central to the question. Therefore, "obsessive" is the most fitting choice, as it encapsulates the behavior of fixating on minor details.