There are many functions of zinc in human body. Sometimes we have been suffering from Zn deficiency, but we have no idea about its symptoms. So, to mitigate the Zn deficiency it is needed to know the symptoms of it.
You might want to try an online search for a structured literature review on the topic. In the meantime, it is safe to say that most organ systems are involved
Skin, nails and hair
acne, eczema, xerosis, seborrheic dermatitis, or alopecia
(thin and sparse hair).
Mouth
Oral ulcers, stomatitis, or white tongue coating.
Vision, smell and taste
Disturbed sense of smell and taste.
Night blindness
Immune system
Increased frequency of infections.
Inflammatory cytokine levels (e.g., IL-1β, IL-2, IL-6, and TNF-α) in blood plasma affected.
Symptoms such as anaemia, diarrhoea, immune, dysfunction hypogonadism and dwarfism are known to be associated with zinc deficiency.
Zn plays a catalytic role in enzymes from all six classes of enzymes. Evidence of a direct link between signs of Zn deficiency and anaemia, diarrhoea, hypogonadism etc in humans have not been shown, however, an overt physiologic defect occurs when the Zn-requiring enzymes are rate-limiting in a critical biochemical pathway.