Plumage as indicator of health in birds
This resource provides a short list of which general components of plumage are good indicators of a healthy bird.

Your pet's plumage should be. . .
Soft - feathers should be strong, yet flexible.
Smooth - no rough feather shafts; no uneven or split edges
Glossy - sheen extends over the entire coat
Full - thick, where it needs to be
Vivid - color should be deep, bright and uniform
Clean - free of dust, dander, waste, or soil
Parasite-Free - no lice or mites

Also, this website page discusses the signs of malnutrition or disease in plumage in more detail.
Stress bars, dark lines which transect a feather, are directly caused by an inefficient absorption or lack of required nutrients. Stress bars can be found on all feathers during the period of malnutrition, and remain even after this period.
Assymetrical moulting is also a sign of bad health. There should not be any bald patches present during the moult.
The resource states that if a moult is delayed due to malnutrition, an incorrect photoperiod or a metabolic problem, plumage will become depigmented. However, the appearance of &quot;dirty&quot; feathers can also be due to overpreening or damage done to feathers by physical contact.
Finally, a change in the usual plumage color of the bird in question is indicative of a lack  or oversupply of a particular nutrient.