I know what dragon nerd means. Though for breeding recommendations, thing such as appearance would have little to do with breeding, nor movement for breeding, if a pairing needs to occur, as long as both participating institutions follow along, then it will occur.
But i spose for exhibit purposes, if an animal looked unwell, or 'shabby' that animal could be held off exhibit for a while and be given extra attention, ie vert checks, blood smaples, and maybe even a clean. By shabby, or diseased, i asume you mean hair falling out, maybe a runny nose, basically un appealing apperance for the public, and animal may be lacking in a vitamen, and may certainly be tested for it, and supplementted or diet changed for it.
If you were going to import an animal from overseas for education purposes, hence exhibit purposes, most zoos would very well 'select' the best looking ones, as they would not go to the trouble to import an unappelaing animal, but rather asses the animals health and see if its due to diet or treatemnt at the institute it's at- maybe under nourished and you see ribs.
But if an animal did look unwell, and changed in condition before an imidiate move, then it would not be moved, and would be assesed before any de[ature.