What would the difference be?
skill: what do you know to do, an expertise
quality: for a person: nice, quiet, intelligent
Dave, I see them as very different words. Can you give an example of a sentence or situation in which you would be confused about which one to use? That might help us see where your confusion is, and be better able to help you.
Teachers: We supply a list of EFL job vacancies
-He has good qualities as an engineer.
-He has good skills as an engineer.
Students: Are you brave enough to let our tutors analyse your pronunciation?
If he has good skills, then you mean what he has been trained to do and what he has demonstrated he can do. His abilities to analyze, calulate, use the CAD programs, design, etc.

His qualities, as MH has suggested, apply to him as a person. He is hard working, reliable, able to easily develop rapport with the customer, etc. These are not things that he went to school for, but things that are part of his personality.

Does that help?