Discuss the components of Carl Jung's theory of "collective unconscious" that might make this theory challenging to apply.

It is not clear here what you mean by "apply," but I'll address the question in terms of the "collective unconscious" applicability as a theoretical concept writ-large and, at points, briefly discuss its applicability in terms of therapeutics.
Jung understood the collective unconscious as the elements of the unconscious mind which are shared collectively. They are elements buried deep in the human psyche, across cultures and manifest in archetypes and other universal symbols. One sees these symbols, like the "hero" or the "wise old man (sage)," repeated again and again across history, in various artistic and cultural forms. While some aspects of the collective unconscious are easy to see and identify, others are less obvious and more deeply hidden (aspects of what Freud called the "Id," for example). This is one argument for why this theory may be challenging to apply.
One aspect of the collective unconscious as expressed through archetypes involves the various stages of life one passes through. While this may have powerful therapeutic potential and is a cornerstone of analytic psychology, it is also somewhat driven by the idea of an unavoidable life path. Some would say this idea of destiny or fate isn't very scientific.
The theory can also be challenging to apply therapeutically, since it's not really rational. The idea of the collective unconscious is essentially the suggestion that there are deep, powerful, and largely unavoidable forces in the unconscious which affect our behaviors and thoughts. While we all try and forge an individual personality in the interstices of these larger psychic forces, Jung's idea challenges the idea that we have much control over some of the choices we make and things we do.
Much as Jung's collective unconscious seems like a nebulous and intuitive concept that is difficult to prove or support, there are actually all sorts of findings in academic fields, as diverse as anthropology and neuroscience, that show how convincing and comprehensive Jung's concept is.
Try as we might to live in the conscious, nominally rational world, unconscious, irrational behaviors and thoughts continue to bubble up to the surface of our minds and affect our lives.