How is it possible to recognize that another person has some hidden potential? The ability to see what others don't know about themselves may be a talent in itself. Recognizing under-developed traits in others is possibly a sign of maturity that comes with age. Seeing hidden talents may also require several other valuable character traits.
When we've established self-respect, we're in a position of respect others. We will then look for ways they can respect themselves more, admire their accomplishments and expect greater things of their latent abilities. We're on solid ground with ourselves and free to disregard others' caustic opinions of us. We see the harm that comes from pandering for other's approval. We naturally give other's the same permission to be respectful of themselves.
When we understand ourselves deeply, we seem to be several different people inside taking turns at showing up in the world. We realize how we fill different roles without conflict, acting like very different characters in different situations. With this comes a sense of other people we could be and many "right ways to live". We become far more tolerant and understanding of others. We're no longer threatened by differences from us or their deviation from a pretentious norm.
As we get in touch with our feelings, we accept our full range of emotions. We then become more sensitive to others' feelings, moods and vulnerabilities. We become more gracious and considerate of others' feelings. We also then trust our own feelings as a guide of where to make a difference and what to avoid. We give others the sense that their feelings are valuable, informative and essential.
As we tune into other people's world views, we develop multiple perspectives for viewing situations. We can make sense from varied points of view and imagine others doing the same. We can then empathize with ways of seeing a situation unlike our own. We allow others to comprehend their challenges with their own frames of reference for starters. We give validation before education. Stephen Covey advises, we "seek first to understand, then to be understood".
Taking tall this into consideration, it seems that our ability, to see hidden talents in others, emerges with the development of our own talents.